Not likely. I suspect Cha Faile will go on to become the beginning of an intelligence service that serves whatever realm Perrin and Faile end up ruling. Faile was already using them as spies, and Balwer started providing his expertise.

The remnant of the Aiel will be whichever ones survive the LB. I believe it will include at least Aviendha, Amys, Gaul, Bain and Chiad. Possibly Rhuarc, though he could very well die as well. The gai'shain will probably survive, possibly the Aiel who've settled in Rhuidean.