With Rand knowing balefire is the only permanent way to get rid of the forsaken, and all the time Nyn spent around Rand, I bet someone at the tower knows. Nyn is at the tower after all.
The only thing I don't remember off the top of my head is whether or not Rand learned that before or after Nyn...
I took what happened to Mesaana as more of a natural labotomy. She did not go insane, her mind broke and scrambled like eggs. If Nyn couldn't heal Rand's madness I doubt she could heal this. Anything is possible, I just dont really see it happening. The Aes Sedai already had one chance at a...