Somehow, I think Elaida is in the group of Aes Sedai that will be lost to the White Tower forever (especially since the Outrigger novels will not be written). The problem with the Seanchan is their structure - they will try and most likely succeed in breaking Elaida, re-naming her and then after this, she'll be asked to demonstrate everything she knows. Unfortunately, with the entire Empire being in chaos, by the time they get around to having her show them this weave, there won't be any way to consolidate the Seanchan forces to act on the information - the lack of a leader in the homeland is going to prevent them from organizing. Also, as you said, Elaida is all kinds of an idiot, but she is incredibly strong-willed, and she may potentially take a long time to break to the point where she would betray the White Tower and her Sisters.

I'm of the opinion that what may happen is that Egwene will realize that she has a ticking time bomb situation on all fronts, and she may offer Fortuona the opportunity to Travel with all of her forces to Seandar in order to consolidate her rule in exchange for neutrality with the Tower. The White Tower Aes Sedai may very well fight for Fortuona in Seandar leaving Rand free to worry about Tarmon Gaidon without the Seanchan over his neck.