Speaking of Constantine. If baptism is needed to be saved, then the RCC was ran for around 31 years, by a man without any of the "infused righteousness" of Christ. So, was he wasn't even part of the invisible church. Not really a Christian, if baptism is needed for acceptance into God's Kingdom.The problem with your theory (and it's really more wishful thinking than a theory) is that there is no evidence of a schism before 1054. Neither is there any evidence that a new church sprang up around the time of Constantine. There was one church before Constantine. There was no schism during the reign of Constantine. There was one church after Constantine. It was the same church before and after, except it was quite a bit larger after Constantine.
If there had been one church before Constantine and two churches after Constantine you might have a credible theory, but there were not.
Every church historian with any credibility disagrees with your position. Bruce Shelley (Baptist) and J.N.D. Kelly (Anglican) to name a couple. I've heard Leon McBeth (Baptist) takes the same position although I haven't read any of his books and can't say for sure.
Constantine wasn't baptized until right before he died. So, your own Pope must not have been too concerned with the "saving power" of baptism.