The Assyrians were the earliest attested speakers of the Semitic language family. They spoke and wrote Akkadian, and mingled with (and supplanted) the native Neolithic Mesopotamian populations. Akkadian names begin to appear in Mesopotamia by the 29th century. Semitic is part of the larger Afro-Asiatic branch, and all of the other members of the branch originate in Africa. It is very unlikely that the Semitic group (and therefore Assyria) have anything to do with India or central Asia. Even earlier, about 3000 BCE, are the Kish, speaking an East Semitic and overlapping the region of Sumer. There is no connection to your "worshiper of Asur" in Vedic (and I've not heard this term before myself; are you sure you are interpreting it correctly, and in the right timeline?)
The precise origin of the Semitic branch is not known, but an origin in north Africa is likely, specifically between the Nile Delta and the Levant, or perhaps from the Arabian peninsula. Relatively recently, a study has proposed an origin in the Levant, which I also like. online link here. It also maps well with a possible interaction to/relation with the Natufian Culture of the Epipaleolithic (very tentatively).
Edit: now I understand that you are conflating Aššur (hence Assyrians) with the Sanskrit asura. Aššur/Ashur/Assur was the name of the principal city of the Assyrians, on the western bank of the Tigris, but also the name of the state, and the name of the tutelary deity. It was really just a divine form of the name of the city itself (like the goddess "Roma"), but the people of that city (the Assyrians) sort of forced the god Aššur into the pantheon of Mesopotamia and then later other religious systems. With the caveat that I am definitely not an expert on Sanskrit etymologies: the connection between Aššur and asura in Sanskrit is completely coincidental. They are from two entirely different language trees (Indo-European vs Afro-Asiatic -> Semitic)
While the answer is no, I see how you got there. As I described in more detail in that answer linked by u/agent_orange137, "Asura" in the Vedas (and the corresponding "Ahura" in the Avesta) are categories, more than individual gods. In the Vedas, where the word is actually "Asura," it's always a title/category. In the Avesta, "Ahura" is mostly used as part of the name of the supreme Zoroastrian god, Ahura Mazda. It is occasionally used as a title/descriptor for some of the other high ranking divinities like Mithra and Anahita.
Everything described in that paragraph is a product of the Indo-Iranian culture and language. This is the subset of the wider Indo-European linguistic family that produced most of the historic languages of Iran and northern India, as well as many in ancient Central Asia. The oldest literature ascribed to this group is the Rig Veda, attributed to the Indo-Aryan (aka Vedic) subgroup that migrated to India. The Rig Veda was preserved as oral tradition for centuries, but maintained its archaic language and structure. Using predictable linguistic changes as a guide, scholars have typically dated the earliest form of the Rig Veda to c. 1500 BC, probably in Central Asia. The Mittani, a people who ruled northern Syria in the late Bronze Age, also appeared around that time with inscriptions containing language, vocabulary, andl theology very similar to the early Vedic hymns. The thought is that the Mittani ruling class represent another branch of the same migration that brought the Rig Veda to India. Meanwhile, the Avesta is traced with similar tools to about 1200 BC, and is thought to have originated somewhere in region of Afghanistan, Uzbekistan, or northeastern Iran. Over time the Zoroastrian religion of the Avesta spread south and west into the rest or Iranian world.
On the other hand, the high Assyrian god "Asur" has entirely different origins. For a start, when you use the proper notation, the word you might see as "Asur" should usually be "Ašur." That mark over the S indicates that it's intended to be pronounced like we would usually say "sh" in English. So rather than Assur like Vedic "Asura" we should read it as Ashur, lile the Assyrian kind "Ashurbanipal." This is confused and muddied by general conventions like the nation of Assyria, the king Essarhadon, or the city of Assur, which are typically written in a way that leads English speakers astray from the original Akkadian. In every case the stem is actually the name of the god "Ašur."
Ašur originated as the patron god of the city of the same name (Assur), first mentioned in Akkadian sources c. 2000 BCE. Over time he was equated to the primary gods of neighboring cultures, and was proclaimed as King of the Gods with the first Assyrian Kingdom in the 1800s BC. That means Ašur was first 300 years before the first Indo-Iranian migrations to the Near East and was first recorded 500 years earlier, not long after Indo-Iranian separated from Indo-European.
The last major point to make is that the Assyrians,and thus Ašur, belonged to the Semitic linguistic and cultural family rather than Indo-European. Their myths, language, and religion shared traits with the Akkadians of central Mesopotamia, the Amurrites and later peoples of Babylon, Canaan, Hebrews, and Arabia.
In short, nether Ašur nor his people had any ties with the Indo-Iranians. In fact, they significantly pre-date their presence in the same region.
Not to distract from any potential answers that may come, but a similar question was asked some time back. . You might be interested in the response given there by u/Trevor_Culley