IMO, it would be pointless to include yet another plotline concerning Fain trying to get a power base to harm Rand (of course without success in the end), especially such late in the game. While Fain was an important factor in the past, I think now Fain's plotline just has to be concluded by his death (like Masema's, for example), namely through the Darkhounds and/or Slayer.

There is also the following Q&A on Fain's powers after SL is gone:
Week 10 Question: "Now that Shadar Logoth is gone, (cool way to get rid of it by the way), has the evil power in Padan Fain/Mordeth/the Ruby Dagger decreased any? Has it driven him even more insane? Or since the next book is called the Knife of Dreams, will all these questions be answered in it?"

Robert Jordan Answers: "The evil power in Padan Fain has neither decreased nor increased, nor has that in the dagger. The corruption in him was partly caused by the taint on Shadar Logoth, but it didn't constitute a real connection to the city. Remember that it was because he was Padan Fain, the Hound of the Shadow, that he was able to leave Shadar Logoth in his new condition after he merged with/absorbed Mordeth. (By the way, any other artifacts that might be lying around from Shadar Logoth would have the same long-term corrupting effect as the dagger. Fortunately, or unfortunately, any such thing would need to be metal or stone. The wood and fabric had decayed. It wouldn't have been pleasant to get a splinter from, say, a chair from Shadar Logoth.)

The destruction of Shadar Logoth has not driven Fain any more insane. I'm not certain he'd be able to function at all if he were any madder than he already is. But being insane doesn't make him any less dangerous, only less predictable. He no longer responds to situations or events in any sort of sane, logical manner. His abiding concerns are hatred of Rand al'Thor (and to a lesser degree Mat and Perrin) because he blames them for what the Dark One did to him in order to turn him into the Shadow's Hound, and hatred for the Dark One because of what the Dark One did to him. He goes after Rand because Rand is the easiest target in his mind, but if he can take a swipe at the Dark One or the Dark One's minions in some way that he felt would cause real harm, he'd leap at it."

But RJ also said "that Fain is essentially his wild card, a character that is outside the structure of the work and can therefore act totally unpredictably."

Since the ending (i.e. Rand's fight against the DO) is naturally a main part of the structure of the work, it's pretty clear that Fain won't play a crucial - gollum-like - role at TG.