A fair number of Roman nobles did in fact convert to Judaism (some of whom are mentioned in the Talmud - including the great Jewish sage Onkelos, who was in fact the nephew of Titus Flavius), and it's strongly suggested that Constantine converted to Christianity (and led the Roman Empire to do the same) not out of real spiritual belief but purely as a strategic move to unify the Empire under a single faith (hence the Nicene Council, as well). I've heard speculation that he was considering converting to Judaism at first, but objected to the requirement for Jewish males to be circumcized.
What if, though, he *had* adopted Judaism as the official religion of the Roman Empire? What would have followed?