So, I defeated him and his minions in that elite hunt on my New Game Plus playthrough (where I'm Level 90... well, Level 92 by the endgame). His gang seemed to die, and he falls into the Sandsea and either drowns or is killed by the Yensa.
But he and his minions do return in the sequel.
My question is this: Does the sequel mention his defeat at the Nam-Yensa Sandsea? Because the player can beat Vayne without beating Ba'Gamnan. I did on both playthroughs, I didn't fight Vayne after Ba'Gamnan yet this time but even at Level 92 he was doing enough damage for Penelo to have to cast Cura on a regular basis. (Archaeoaevis is far worse though, even at Level 92 I had characters die from their attacks, fortunately that's not the path you need to take to get to Ba'Gamnan)