The rift might be less wide, but there might still be a rift.
Blood Elves and High Elves split apart well before the Blood Elves joined the Horde. The rift between them was already there.
Likewise, the Void Elves were exiled because they researched the Void - it had nothing to do with the Alliance at first. They joined the Alliance later on in the questline because, well, the story demanded that they do. But, they already hated each other before Alleria even met them.
As far as High Elves and Void Elves, that has had almost no development. We'll see how they treat each other in the future, if Blizzard remembers that High Elves exist.
So...no, not much would really change, because they all split apart from each other before one faction ever joined the Horde, and before another faction even thought about the Alliance.