No, absolutely not. In fact, in the case of Quirinius' census of Judaea in 6/7 CE, it would entirely defeat the purpose of the census. That occasion was prompted by the fact that Judaea was made part of the province of Syria, under direct Roman rule, following the expulsion of Herod Archelaus in 6 CE. The reason for the census, as explained by Josephus (Jewish antiquities 18.1( was to take stock of the region's population and assets for taxation purposes (as well as for appropriating Herod's personal assets). If such a census registered people for taxation in places they weren't living, it would be totally pointless.

The motif of people going back to their hometown comes from two considerations.

1. Seeking precedents in the Hebrew Bible. The two birth narratives in Matthew and Luke justify their twists and turns by presenting them as though they are repetitions of bits of the Hebrew Bible. For example, the presentation at the temple in Luke 2: that absolutely was not a thing. What's going on there is that the passage is a mash-up of three bits of the Hebrew Bible -- the offering of two turtle doves comes from Leviticus 12.2-8, the redemption of the firstborn child from Exodus 13.11-14, and the presentation itself comes from Hannah handing baby Samuel over to the temple in 1 Samuel 1.22-28.

So there's no need for precedents in any kind of Roman practice, because the author of Luke wasn't interested in Roman precedents. The important precedent was the first census of Israel as described in Numbers 1.1-4. And that census is described as counting people 'in their clans, by ancestral houses, according to the number of names, every male individually ... A man from each tribe ..., each man the head of his ancestral house.' Luke 2 sounds like it's attempting to echo this passage.

2. Jesus' birthplace as a theological problem. The question of where Jesus came from seems to have been a matter of active debate among 1st century Christians. The canonical gospels are perfectly clear that he came from Galilee; but in some quarters, at least, there was a messianic expectation (based on the Hebrew prophetic book of Micah 5.2, which Matthew quotes) that he ought to have come from Bethlehem. John 7.41-42 reports a dispute along precisely these lines: there the people are complaining explicitly about the fact that Jesus comes from Galilee, not Bethlehem.

In this light, it's pretty clear the settings -- birth in Bethlehem, growing up in Galilee -- are designed to appeal to both sides of the debate. He came from Galilee, as everyone knew, but supposedly he had actually been born in Bethlehem. The three gospels that address this solve the problem in totally different ways: in Matthew the family lived in Bethlehem, and only moved to Galilee to escape the clutches of Herod Archelaus; in Luke we get the spurious census; and John simply reports that there was a debate over the matter, as I mentioned.

So, TL;DR: there was a problem with Jesus' actual origin conflicting with where the Messiah supposedly ought to come from. The author of Luke solves it by appealing to precedent from the Hebrew Bible.

I've written about this before here on AskHistorians and also a longer piece on my own site: it may be you'll find something further of use there.

Incidentally, the idea of a census 'of the whole world' is probably based on a different kind of census, the censuses taken of Roman citizens across the entire empire in 28 BCE, 8 BCE, and 14 CE. Just note that (a) none of those is within earshot of a sensible date for Jesus' birth, (b) Judaea and Galilee weren't under Roman rule until 6 CE, (c) Roman citizens outside Italy were people living in colonies sent from Italy, not people who had been conquered; and (d) trying to link any of these censuses to the one in Luke 2 would mean arguing that Joseph and his family were secretly Roman citizens, which is obviously nonsense.

Only the most ardent literalists would suggest anything historical about Luke's census. Mainstream Bible commentaries, including those written by and for practising Christians, are perfectly happy to point out that the census raises 'many virtually insurmountable problems' (Oxford Bible Commentary, ed. Barton and Muddiman, 2001, p. 928). If you're really interested in reading as much as you can about the birth narrative, the foremost scholarly work on the subject is Raymond Brown's classic The birth of the Messiah (1977), again, a book written by a practising Christian.