Well, the people in Oman rebuilt quickly, so you’d have to read “the whole world” in the same way it’s used when Luke claims “all the world” participated in the census. But yes.
Luke records that Caesar Augustus gave the command that all the world be registered. Caesar probably meant all the Roman controlled world and any other place the census-takers found.
The Roman god-ruler said what he meant...EVERYWHERE. I don’t know how far they got.