Impossible to say really. While he achieved impressive longevity in his own era, I think that his life style would catch up with him against Louis's opposition, even if he was as good as they say that he was.
With no film of Sullivan nor any real knowledge of his actual opponents it’s hard to gauge how he’d do in a different setting like the 1930’s-40’s etc. if he’s well trained and in shape he might have beaten some of Louis’s opposition but I’m really only giving him the benefit of the doubt without anything to back it