Rand would not be where he was today if the Tower had not split. In the first few books only a very few Aes Sedai knew what he was and who he was. At the end of TGH he was starting to become known but he had not gathered a large army around him so the Aes Sedai as a whole could not move to either sever him or control him.

Next he finally takes control of a nation in Tear but before any organised expedition can be sent from Tar Valon he had gone to the Waste. As far as the Aes Sedai are converned he has dropped off the radar. Then the Tower splits just in time to allow Rand to return to the Westlands.

Had the Tower not split one of two things would have happened. Siuan would have kept control but would have been under extreme pressure from the Hall and the Ajah's to get Rand under control. As far as I can recall she was all for controling him anyway. It was Moiraine who realised Rand needed to run free. Option 2 is that Siuan is overthrown and the Tower rally behind the new leader who will move heaven and earth to get control of Rand. Its not hard to see a force of 300 or 400 Aes Sedai being sent to bring Rand in and at this point the Aiel would not be too keen on fighting Aes Sedai.

Rand would very quickly have ended up at best with a committee of Aes Sedai advisors telling him what to do, what to say and when to say it or at worse he would find very nice and very well guarded guest quarters in Tar Valon. There certainly would be no Black Tower, no Asha'man, no cleansing of the Taint etc.

I don't think its a conincidence that the Tower is only reunited at a point in time where Rand and the forces he commands is now more powerful that the combined Aes Sedai. The only groups that can challenge him are the Seanchan and the Shadow.