No, but there was the possibility for a Kurdish state just after WW1.

After the end of World War 1, Ottoman territory was carved up by the allied powers. This can be seen in the borders of the middle east (Syria, Iraq, Jordan, Lebanon), which were largely determined by the Sykes-Picot agreement. These newly formed countries were called League of Nations Mandates, and European powers were to govern them until they were properly 'civilized.' France got Lebanon and Syria, England took charge of Iraq and Jordan. Palestine was meant to be a joint administration, but was effectively a British protectorate. Italy controlled Libya.

This was to be the case with Anatolia as well. The Treaty of Sèvres (1920) was to be signed between the defeated Ottoman Empire and the Allies, but it was never ratified. It gave parts of Anatolia (Modern Turkey) to Greece, Italy, France and Britain, and it chartered an Armenian state, which became part of the Soviet Union in 1922. It also laid plans for the possibility of a Kurdish state. This possible Kurdistan, however, was limited to Anatolia, and thus excluded about 2/3rds of Kurds from its borders.

Whether this state would have been established if the Treaty of Sèvres was ratified, we'll never know. The Allies had broken similar agreements with the Arabs (Hussein-McMahon correspondence), and the Jews (Balfour Declaration). It should be noted that in these cases, however, Hussein's descendants came to rule Iraq and Jordan, and Israel was established as a state after WW2. But in the Kurds' case, the Treaty of Sèvres failed because the Ottoman empire was dismantled internally by Ataturk's rebellion. This rebellion was successful and led to Anatolia becoming modern Turkey, instead of being split between the allies. These borders were formalised in the Treaty of Lausanne (1923).This of course meant no Kurdistan, though there were Kurdish rebellions in Turkey, with big ones in 1925 and 1927-1930, which were brutally repressed.

As to your question of whether the lack of a Kurdish state is due to colonialism. I'd have to go with a 'kind-of.' After WW1, a Kurdish state could have been established. The Kurdish state in Anatolia didn't happen because of Ataturk, but outside Anatolia new states were determined by the Allies, and Kurdistan was not one of them.

Sources: Cleveland, William L. and Martin P. Bunton. A History of the Modern Middle East. Boulder, CO: Westview Press, 2013.

Yapp, Malcolm. The Near East since the First World War: a history to 1995. London: Longman, 1996.

tl;dr: Kurds had the bad luck of being between the Ottoman and Persian Empires, sort of like the Poles of the Middle East. Like the Poles, there was also hope for their national ambitions in the aftermath of World War I. Such was even promised in the 1920 Treaty of Sevres, and would have likely ended up including both Southeastern Turkey and Northern Iraq, as this was a great period of redrawing of borders. Poland emerged,however, in part because neither Russia nor Germany was able to reconquer until 1939 (Russia tried in 1919 though). Kurdistan was not so lucky--Turkey was able to reassert military control over the entire region between 1918-1923, with the British then deciding to keep the oil rich Kurdish section of Iraq. After the slaughter of World War I, France and Britain were willing to expend neither blood nor treasure to ensure the independence of this hilly backwater, nor indeed were they willing to defend its promised neighbor, Wilsonian Armenia. There were periodic rebellions against Turkish rule through 1938, several major, but none managed to overcome the serious internal Kurdish divisions. Glancing at these maps might help, as well as glancing at this Ottoman-Safavid map and this map of the expansion of the Ottoman Empire.

• Part One: Age of Empire against the Rise of Nationalism

There were three great Muslim Gunpowder Empires: the Ottomans in the Balkans and Anatolia, the Safavids in Persia, and Mughals in India. Like Poland, long stuck between Russia and Germany (and Austria, and Sweden), "Kurdistan" was trapped between the expanding Ottoman Empire (who came to the region in the 16th century) and the Safavids (whose dynasty was found in 1501 by Shah Isma'il, who's a fascinating historical character in his own right). The thing is, identities like "Kurdish", "Arab", "Turk", "Persian", "Laz, things that are so basic and obvious to us, were not so important then. Muslim-Christian-Jew (and after Shah Ismail, Sunni-Shi'a) mattered much more. For instance, Shah Ismail was born a Muslim in Ardabil in the part of Iran known as Azerbaijan (the modern state of Azerbaijan makes up only a small part of the historical region of Azerbaijan, and encompasses only a portion of ethnic Azeris, who mainly live in Iran), and people have claimed he was a Persian, a Turk, and Azeri Turk. He almost certainly grew up speaking local Azeri Turkish and an Iranian language (possibly Kurdish, possibly Persian). But it's important to remember that he was also the great grandson (through his mother, so it doesn't count) of Emperor John IV of Trebizond. Trebizond, of course, the last Greek state in Anatolia. Constantinople fell in 1453, Trebizond (modern Trabzon) fell in 1463--both to the Ottomans.

Between the expanding Ottomans (who were already to the Eastern Black by the second half of the 15th century) and the consolidating Safavids (who managed to keep much of the structure and size of the Timurid Empire which ruled Persia before them) lay a series of Kurdish Principalities. They were in no way united (as the Turkic tribes in Anatolia had not been united between the collapse of the Seljuks and the rise of the Ottomans), meaning there was never a single Kurdish state. Between the 16th and the 19th centuries, all of these were eventually absorbed by either the Ottomans or whichever dynasty ruled Persia (the big two dynasties being the Safavids 1501-1722 and the Qajar 1785–1925, with the three dynasties between them being remembered like the three Soviet leaders between Krushev and Gorbachev).

Western Europeans played relatively little role in this part of the world until the 19th century. Russians only really arrived in force towards the end of the 19th century (see the Russian conquest of the Caucasus), though ended up winning several wars against the Ottomans and against the Persians. Britain, France, and Russia all increasingly meddled in both internal Ottoman and Qajar affairs during the 19th century--much to the consternation of the locals. The embarrassing capitulations were two of the things that stoked nationalism within the empire, and encouraged the dominant groups in both states to stage constitutional revolutions. Both were shorted lived, with the First Ottoman Consitutional era lasting only 1876 to 1878 and the First Iranian Constitution only lasting between 1906-1911.

So the Kurds were caught between the feuding Ottomans and Persians, who fought at least ten wars between the 15th and 19th centuries. Nationalism came relatively late to the region. The earliest forms of "Persian nationalism" were the people united against the Qajars and European powers, things like the Tobacco Protests and the movement that led up to the Constitution of 1906, were quite inclusive actually and included both Persians and Azeris (and presumably Kurds). Even today, Iranian nationalism is quite civic, like France perhaps. Turkey's post-1923 nationalism, by contrast, is much more ethnic, like Germany's. CIA World Factbook estimates Iran is Persian 61%, Azeri 16%, Kurd 10%, Lur 6%, Baloch 2%, Arab 2%, Turkmen and other Turkic tribes 2%, other 1% (including Jews and Armenians). There's relatively little ethnic conflict between the Azeris and the Persians, especially if you compare Iran to its neighbors: Iraq, Turkey, Azerbaijan, Turkmenistan, Armenia, Afghanistan, and Pakistan, all of which except possibly Turkmenistan have had recent major ethno-national conflicts. If there were a moment when the Iran could have broken up and a Kurdish state somehow emerged, it would have been if the first decade of the 20th century had been different for Iran. Russia and the UK literally had divided the country between (see the Anglo-Russian Convention of 1907, which could have been a Sykes-Pikot of Persia). Here's a map of what they agreed--Russia is blue, Britain red, the yellow is a neutral buffer zone. This isn't as absurd as it sounds today--Russia had recently acquired several Muslim areas in Central Asia and the Caucasus in the 19th century, and Britain controlled neighboring (East) Balochistan (now part of Pakistan) and the Balochs are an Iranian people, about 4% of modern Pakistan and 2% of modern Iran. Why not Iran, too? I'm getting lost. Anyway, this was the moment that Iran could have been carved, and this in this carving up there is the potential that a Kurdish area could have potentially emerged (just as Druze, Jewish, and Christian areas had the potential to emerge when France and Britain carved up the Arab regions of the Ottoman Empire--only the later two did, as Israel and Lebanon). For my money, the most interesting character in this whole deal was Morgan Shuster an American (!) hired by the new Parliament of Iran to get their finances in order. The government getting their finances in order was exactly what Russia and Britain did not want, and Russia went as far as to shell the Iranian Parliament to get him out (well, and to exert hegemony more generally, but it's a better distant prequel to Argo if it's just about one man). The point is, the borders of the modern state of Iran are almost identical (if not totally identical) to the borders of Persia at the end of the Qajar empire. Nothing could break off.

The Ottoman Empire is a very different story. While people tell the tale of the Ottomans as the "sick man of Europe", nationalism is what actually did the Ottomans in. Except for the Caucasus (which fell to Russia) and North Africa (which achieved independence and was eventually all taken by European powers, Libya last, in the same generation that saw the end of the Ottoman Empire), nationalism is what peeled off bits of Ottoman territory. Before the mid-19th century, few Ottomans would call themselves Turks. Turks were lowly country people, or the unsettled nomadic groups outside the empire. Remember how I said earlier that identities like Turk, Arab, Persian didn't matter in Shah Isma'il's time? The mid-19th century is the period they begin to matter. The traditional date for advent of modern nationalism is 1789, with the French Revolution creating an idea that the governments stand for a (clearly delineated) people, and that the borders of the cultural unit ("the French people") should be identical to those of their state ("the French state"), creating the first nation-state. These nation-states were justified not by divine right or something like that, but because they ruled in the name of the people. (for more, see one of my older pieces on "Why is nationalism considered modern?"). Nationalism in the Ottoman Empire moved West to East, North to South, and Christian to Muslim. The first groups to rebel and demand their own nation-states Greeks and the Serbians (though it's ambiguous when those states meet the modern definitions of nation-states rather than independent states--both may have had imperial ambitions of their own initially; that is, they wanted their borders to include subject peoples from outside of their cultural group). Armenian nationalism picked up in the late 19th century (see events like the Armenian Dashnak Takeover of the Ottoman Bank in 1896). Arab nationalism picked up slightly later than that. Before Turkish nationalism really took off, there were several aborted intellectual movements like the Young Ottomans that advocated either a Pan-Islamist or Pan-Ottomanist approach, rather than a specifically Turkic orientation. These groups tended to be led by Rumelian (European) Turks, and had success recruiting some European Muslims (including Turks and Albanians) but little success in other regions.

Depends what you consider a "state". They were independent tribes for a while, then semi-independent chiefdoms which were puppets of the Ottomans and Persians. Eventually they were incorporated into the Ottoman and Persian Empires. Kurdish nationalism as we know it today developed in the early 20th century during the decline and fall of the Ottoman Empire, about the same time as Arab nationalism was also on the rise. After WWI ended, Britain and France began carving up the Ottoman Empire, and there were proposals for a Kurdish state, with one making it into the (ultimately abandoned) Treaty of Sèvres.

There were also a few short-lived tries to establish a Kurdish state through armed rebellion: one called the Republic of Ararat, during a 1927-1930 rebellion against the Turks, which was ultimately crushed by the Turkish military. There was apparently also one in Iran (or 'eastern Kurdistan') in the 1940s called the Republic of Mahabad or the 'State of the Republic of Kurdistan'. It was even more short-lived, lasting only from 1946-1947 before being put down by the Shah, its leaders either executed or fleeing to the USSR and Iraqi Kurdistan.

Ultimately I think the biggest reason the Kurds have never had a long-lasting state of their own is simply that they had the bad luck to be located between larger, more powerful empires (and later nations), especially the various Turkish and Persian powers. That and the fact that the modern idea of the nation-state didn't really have any currency in the Middle East until the early 20th century.

Incidentally I think they're closer now to having a state than they've ever been. The chaos in Iraq and Syria has allowed them to demonstrate their independence by defending their own territory and governing themselves. With Saddam and now Assad off their backs, they're running the southern part of what they consider to be Kurdistan as an independent state already, without waiting for international permission or official recognition.

Taking your term "ever" literally, Kurdistan was actually a collection of states.

Kurdistan in the Middle Ages was a collection of semi-independent and independent states called "emirates".

This is a great question. There's a Kurdish "region", Kurdish principalities/chiefdoms", and in Iran the province of Kurdishtan. But nothing autonomous.

Yeah they have kind of, during the collapse of the Ottoman Empire they established the Kingdom of Kurdistan but it was never recognised and it only lasted a few years. Then after WW2 they established the Republic of Mahabad which was effectively a Kurdish Soviet puppet, that lasted a few years also until it was eventually annexed by Iraq in 1947.