Something tells me that it will at the very least be more complex than the story of Gollum. One thing to remember is that Bilbo and Frodo left Gollum alive through pity - Rand has always tried to kill Fain whenever he has seen him.

But Fain might well be used to help seal the Bore, though I think Saidin + Saidar is more useful in this regard.

One possibility is that assuming Rand survives TG, Fain appears AFTER as a sort of "miniboss", perhaps taking control of the Two Rivers like Saruman did with the Shire.