Fundamentally if you change just about anything in history, you change a lot. I'm a tremendous nerd, and one of my interests is a form of speculative fiction known as alternate history; the very basis of this sort of fiction is the question of "What if?". In the world of alternate history there tends to be talk of "butterflies", it refers to the butterfly effect, often associated with science fiction involving time travel. The basic idea is that even a minute thing can cause massive consequences and cascading cause and effect.
For example, let's imagine that Archduke Ferdinand survived the assassination attempt, that's a pretty big thing that could cause pretty big changes. But let's use time travel as a thought exercise: What if I built a time machine and when I travel back in time, I step out of my machine and step on a bug. That may seem inconsequential, but what if someone else was going to step on that bug, and it caused them to have to clean their shoe later, which made them five minutes later; but now that doesn't happen, and they arrive five minutes earlier, and we have a chain reaction of cascading causes and effects rippling out. And oh, by the way, because you stepped on that bug
Stanislav Petrov wasn't there to stop World War III from happening back in 1983.
So from that perspective, of course things would be different without Paul. But that's true not just of Paul, but of everyone else in the early Church. That doesn't mean that without Paul there is no Christianity at all as we know it, because if we are of the position that what Paul said and taught was the same as what the rest of the apostles taught, then that teaching is still there.
But let's consider some of those butterflies:
There is often a general agreement that one of the main motivations for the defining of the Biblical Canon is as a response to Marcion of Sinope and the Marcionites. See, Marcion is considered the first person in the history of Christianity to attempt to create a defined Christian Canon; to deal with Marcion it was necessary for the Church, in response, to talk quite seriously about a defined Canon. The thing about Marcion is that for Marcion the only true apostle was Paul, and Marcion's Canon consisted only of a heavily edited version of the Gospel of Luke, and edited versions of Paul's letters.
When we remove Paul, we remove Marcionism and Marcion's Canon, and so then what happens? Is there something else which spurns the Church to act to deal with a defined Canon of Scripture? It's pretty likely that something probably would happen, but definitely in not the same way. And obviously without Paul the Canon is going to look very different. For one, without Paul we don't just not have the Pauline letters, we also don't have Luke-Acts. Would there, then, be three Gospels instead of four? But it doesn't stop there, because we can also talk about 2 Peter and Jude; both of which are likely to have been written sometime in the 2nd century. Now, if Jude influenced 2 Peter, it is possible we'd still have Jude, but if 2 Peter influenced Jude, then the existence of both is hard to say. At the very least, the content of 2nd Peter would be different.
Speaking of Peter, how would things have gone had Paul not been there to rebuke Peter when he shied away from eating with the Gentiles when the group from Jerusalem visited?
None of this is to say that the core confession of the Christian religion would be different, because we accept on faith that the apostles were in concert with their confession, and so the apostolic confession would still be delivered even without Paul. But even if the apostolic confession remained, that doesn't mean things aren't going to be seriously different.
Take Paul away, and watch as the butterflies pile up.
-CryptoLutheran
