I think that if Gandalf stayed with the Fellowship the Fellowship would have still broken up. Gandalf would want Aragorn to go and help with the coming war so Sauron would be distracted by the return of the king rather than finding the ring. I think that Merry and Pippin would still have been captured. I do not know whether or not Borromir would have fallen or not. Either way the Fellowship would have split up. Gandalf would have asked that Aragorn, Legolas, Gimli, and possibly Borromir to go save Merry and Pippin. After they save Merry and Pippin (if they could) they would not try to catch Gandalf, Frodo, and Sam instead they would go and aid in the war. Gandalf would have helped Frodo and Sam get into Mordor but after they got in he might disappear so that Frodo and Sam would meet up with Gollum. Gandalf would do this because he knows Frodo doesn't have the strenghth to destroy the ring by himself, he needs the help of Sam and Frodo's pity of Gollum. Frodo and Sam would have never met Faramir in Ithelin

but, on the contraray they would not have met Shelob near Cirith Ungol. I think Gandalf would have tried to cross into Mordor over the Mountians of Shadow where the river Poros flows down. The crossing might be easier here because of the river. It is also here that he might have been "promoted" to Gandalf the White by Eru through Ulmo. Is this where he would leave Frodo and Sam as well? I think after Frodo and Sam get into Mordor the plot would be pretty close to the real plot.