Absolutely. Constantine’s vision before the battle changed the course of the west for sure and Christianity itself. But in my own opinion, Constantine would have never existed if Hannibal had sacked Rome 600 years before the Goths sacked Rome.
You’re obviously correct about Hannibal and Rome. But it is tough to pick out a battle to explain why he never took Rome. Dertosa, maybe? Or perhaps Baecula. If Hannibal’s loser brother Hasdrubal had been able to win either battle, he could have reinforced his brother in Italy and things might have turned out differently.