There was a lot of interest among historians of the Crusades in this exact question about 10 years ago, but the evidence since then suggests that crusading and medieval colonialism were more like neighbouring ideologies rather than one being a forerunner of the other. Generally speaking, the Crusades were not the trial run for colonialism. That being said, there was ideological overlap between crusading and medieval colonialism and there were crusades that seem to have had a colonialist intent behind them.

Colonialism in the Middle Ages was largely the result of taking the idea of 'civilisation' from the classical period and revitalising it for the medieval world in order to justify a few wars. The basic version of this was that civilised people made cities and knew God, which produced a Latin Christian citizenship and organised political hierarchies, and that this was the natural progression from primitive barbarianism to cultured civilisation. By conquering barbarian peoples and forcing them into the trappings of civilisation (particularly urbanisation and Latin Christianity, but also things like fashion, fighting style, music, participation by the aristocracy in tournament events etc.), the conquerer was seen to be doing the conquered a favour. The biggest proponent of this medieval colonialism was Gerald of Wales, who uses it to justify English campaigns in Ireland and Wales. Here's a taste of what Gerald was writing:

"The Irish are a rude people, subsisting on the produce of their cattle only, and living themselves like beasts - a people that has not yet departed from the primitive habits of pastoral life. In the common course of things, mankind progresses from the forest to the field, from the field to the town, and to the social condition of citizens. But this nation, holding agricultural labour in contempt... lead the same life their fathers did in the woods and open pastures, neither willing to abandon their old habits or learn anything new."

"For although they [the Irish] are richly endowed with the gifts of nature, their want of civilisation, shown both in their dress and mental culture, makes them a barbarous people. For they wear but little woolen, and nearly all they use is black, that being the colour of sheep in this country. Their clothes are also made after a barbarous fashion. Their custom is to wear small, close-fitting hoods, hanging below the shoulders a cubit's length... This people then is truly barbarous, being not only barbarous in their dress, but in suffering their hear and beards to grow enormously and in an uncouth manner... indeed, all their habits are barbarisms."

(If you want to know some context about Gerald of Wales and his anti-Irish sentiments, I wrote an answer on that a about a month ago here)

It was also used to attack the Scots, though that's after Gerald's time. English policy toward Ireland at this time was changing, with John in particular trying to supplant the local population and settle Ulster with English people and drive out the locals, in contrast to earlier campaigns in Ireland where Norman noblemen had simply taken over or even intermarried with the locals. John's policy wasn't very successful (his interest in Ulster was short lived in the grand scheme of things), but it was the start of a policy toward Ireland that the English monarchy would try again with more success over the following centuries. Gerald of Wales' writings were absurdly popular in western Europe, and went a long way in establishing early colonialist ideology, or at least the British version of it. You will of course note that medieval English campaigns in Ireland were not crusades. This pretty strongly refutes the idea that the Crusades were a straightforward forerunner of colonialism, because you didn't need to be fighting a holy war to be colonialist.

It is also worth noting that medieval colonialism was toothless against the Muslim population of the Middle East. They were, if anything, more urbanised than most areas of Christendom, and although crusaders had little knowledge of Islam and even less desire to learn about it, they could at least recognise the piety with which Muslims worshipped their god. It is rare to see Muslims portrayed as primitive or uncivilised in chivalric literature. Instead, Muslims were often portrayed as the mirror image of Christians, which in a lot of ways they were. Both the Muslim and Christian worlds had equestrian aristocracies, both had similar political structures, similar social values, similar fighting styles, similar mercantile interests and so on. This was actually a pretty big problem for the early Frankish settlers, because they had a habit of getting a bit too friendly with local Muslims and some people thought the Franks were losing their Christian identity. The Council of Nablus in 1120 banned sex between Christians and Muslims within the Kingdom of Jerusalem, and required that they dress differently. How successful this policy was is debatable (where would they even find the manpower to enforce dress codes across an entire kingdom!? And good luck regulating sex) but it shows that the priority of the rulership was not to replace local culture with western European culture, but to protect their own from assimilating into the local population, and it largely failed. By the middle of the 12th century, the region was forming its own hybrid culture rather than a Latin Christian one, much to the concern and anger of crusaders who were expecting Christians in the Crusader States to be just like themselves.

There is also the issue that the Crusades in general did not have a clearly articulated goal, and most crusaders weren't in it for money or power. They realised after the Second Crusade that it was rare to find either by taking the cross. Most likely, you'd die. The earliest mission statements regarding the broad purpose of the Crusades come from Urban II's speech at the Council of Clermont, in which colonialist ideas do not come up at all (he seems to have just wanted some people to go help the Byzantine Empire fight the Turks). There is then a participant of the First Crusade who wrote the Gesta Francorum, our main source for the expedition, who states that he was there to 'destroy paganism', but doesn't go into detail beyond that. Most later crusades were about retaking Jerusalem, not colonising the Holy Land.

But there was some overlap between crusading ideology and medieval colonialism. The Franks did drive out the Muslims from Jerusalem, but we know that other cities like Acre had sizeable Muslim populations, and the countryside also had a large Muslim population and Jerusalem itself seems to have been an exception and far from the general rule. We know that Christian and Muslim noblemen sometimes hung out socially at each others' courts, for example. This is not the behaviour of people driven by proto-colonialist ambitions. I'm sure that many crusaders did have colonialist ideas - we can see that in the expulsion of Muslims from Jerusalem - but they don't seem to have been the majority and these policies were ineffectual. In any case, the archaeological evidence (particularly the excavation of churches) suggests that Latin Christians weren't even close to the majority, and they do not seem to have had a general policy of driving out, replacing, or assimilating native populations. If they were trying to be colonialist, they failed hard.

Crusades in the Baltic, where the locals were sometimes portrayed as barbarians and savages similarly to how Gerald of Wales characterised the Irish, did have some colonialist overtones to them. The preacher and theologian Bernard of Clairvaux declared that the goal of the Wendish Crusade, which was part of the Second Crusade, was to invade the Baltic and occupy it "until such a time as, by God's help, they [the local pagans and Slavs] shall either be converted or erased". I'm sure you can see that, in Bernard of Clairvaux's mind, medieval colonialism and the Wendish Crusade weren't so much overlapping circles of venn diagram, but the same circle with 'Deus Vult' written in it. There is also much to be said for the Reconquista and colonialism, but that's outside my area of expertise.

So while I don't think it's a fair assessment to view the Crusades as a trial run for European colonisation, it is easy to see why some people have that opinion. They were adjacent ideologies that could be made to fully overlap. But you didn't need to be a crusader to be a medieval colonialist, and the typical justifications for medieval colonialism had limited applicability in the context of fighting the culturally sophisticated Muslim polities of the Middle East.

The short answer is no. The history of Crusades historiography is not my strong suit, but as far as I can tell, the idea of the Crusades as “proto-colonialism” is a product of trying to to fit them into the frame of historical materialism, what is sometimes called “Marxist historiography” (though it should be noted that not all adherents of this historical school were on the political left).

This historical frame looks at the past very much in terms of the distribution of material resources and the class conflicts that are believed to result from it. At the height of this school’s popularity, one of the major political issues of the day was colonialism/imperialism. The Marxist view tends to understand colonialism and imperialism as a matter of economic exploitation: a powerful group is driven to deprive a weaker polity of its wealth and resources.

If you are looking for historical analogies to the imperialist moment, then the Crusades might’ve seemed like a decent one. At a broad level, it’s Europeans traveling overseas to seize lands controlled by non-European peoples. Building on this assumption, a Marxist frame on the Crusades will often claim economic motivations for the conflicts. Common claims include that most Crusaders were landless third or fourth sons of nobility, fighting to gain wealth and land, or that Europeans sought to gain control over the Western end of the East-West trade routes. If these claims are accurate, then the Crusades would indeed appear to have some significant similarity to 19th century imperialism.

However, these claims are no longer looked upon favorably by most medieval historians. For instance, many leading Crusaders were not landless aristocrats, but powerful ones: counts, dukes, kings, and even the Holy Roman Emperor got involved in the Crusades. Crusading was also often a very expensive and risky endeavor, too; you’re basically dropping everything to go and fight halfway across the known world, after all.

Beyond that, when we look at the motivations of the Crusaders, economic gain is seldom mentioned. The overwhelming drive of most Crusaders was religious; they were fighting to reclaim and/or defend the Holy Land, and in doing so, repent for their sins. Take, for instance, Palästinalied, a 13th century song by German poet Walther von der Vogelweide. The song is from the perspective of a German pilgrim or Crusader setting foot in the Holy Land. Nowhere in the song is gaining wealth (of a material kind) even mentioned, and when the song directly mentions the fighting, it says Christianity will prevail because its claim is the most just.

An oft-cited, more geopolitical reason for the calling of the First Crusade was to help bail out the Byzantine Empire in the face of Islamic expansion. While not nearly as important for the Crusaders themselves, this does seem to have been part of the rationale for the Church leadership in starting the Crusading effort. This, too, is best understood in religious terms. While there was a certain rivalry between the Eastern and Western churches, the Byzantines were still fellow Christians, and it was the duty of the Western Church to assist its Eastern brothers in their perceived time of need.

Moreover, there was a popular, grassroots response to the Crusades that often took the form of swelling religious fervor. This included men going to join the ranks of a lord’s crusading army, as well as the more disorganized (and generally doomed) peasant’s crusades, including the infamous Children’s Crusade. This should go without saying, but it’s unlikely that children were attempting to march to the Holy Land to get rich. Probably the darkest result of this groundswell of popular religious fervor was mob violence against Jews, most notably seen in cities along the Rhine river during the First Crusade.

While it’s clear there were individual Crusaders driven by greed or ambition (Raynald of Châtillon comes to mind as a possible example of this type), these seem to have been the exception, not the rule. The overwhelming motivation of Crusaders, from top to bottom, was one of piety and religious fervor. As such, the materialist model of “proto-colonialism” is a poor model for understanding the conflicts.

Sources:

A Concise History of the Crusades, Thomas F. Madden, Third Edition.

The Crusades, A History, Jonathan Riley-Smith, Second Edition.