Considering they all believe they were banished to the desert for failing the Aes Sedai (and considering RJ seemed intent on making Egwene the ruler of the whole world, even if it was as a "guiding hand" instead of an outright empress), I wouldn't be the least bit surprised if Aviendha talks the Wise Ones into spilling the secret that only they (and the Clan Chiefs) know. Once they make it clear that the Aiel must take up the Way of the Leaf again, then they'll remind the Aiel that they have a purpose that they have forgotten (and failed in), which is serving the Aes Sedai. Not only will Aviendha hand Egwene the Wise Ones on a silver platter (with them becoming Aes Sedai, if they channel strongly enough), she'll hand her the entire Aiel people, almost all of whom will enslave themselves to the Aes Sedai. That will, in effect, destroy the Aiel, since they will be assimilated into the White Tower (and loyal only to it, since they no longer have a "nation".

The "remnant of a remnant" will be those who refuse to bend knee to the Aes Sedai and choose to, instead, keep their weapons and follow Rand directly (instead of participating in Tarmon Gai'don in whatever way Egwene decides they should). When Tarmon Gai'don ends, what few survive may exile themselves to the Waste again. With only a handful, they'll never really be a real presence again, not for another Age or two, at least.