They don't have the spark. They won't just start channeling randomly one day unless they actually take the pains to learn how. That's how it works. As such, they aren't in danger of being mistaken as damane if they stayed. They were free and clear, if kept from actually wearing the bracelet by Surroth.

The Sul'Dam have see the Seanchan thrown back and defeated several times by the Dragon Reborn. it is conceivable that they don't view the conquest as inevitable and that there are always places to run and hide. after all, in the viewing Rand had of the possible futures, the Seanchan never visited remote backwaters like the Two Rivers. It is possible, if unlikely, to find remote villages to live in that might never be visited by the Empire.

If the white cloaks honestly considered the Aes Sedai creatures of the Dark One, they would not be planning an alliance during the final battle. It is that simple. They see the White tower and Dark one as two completely separate and unrelated powers. Most of their rhetoric is just that, trying to convince people that they're right and everyone else is wrong.

The Aes Sedai represent a different philosophy. Anyone who represents a different philosophy is wrong, and misleading and therefore to be killed on sight. Like many fanatics in religions in the last several centuries in our era.

And I doubt that they would knowingly elect a channeler as Lord Captain Commander. But Galad cannot channel yet. If leads the Whites Cloaks well and gains their respect and adoration, and then learns he can channel, that may just change their minds.