I left the wild Thundurus with 1 hp and asleep, but I don't know if it counts as one turn on the new encounters or if my previous turns carry over. I am using both types of Poké Balls at the moment, and it does not look like any are good. >.<
Despite the fact that you may have been pecking away at wandering pokemon for many, many turns, whenever you meet them, it starts a new battle, from turn 1.
This means that the Quick Ball has twice the capture rate (x4) than that of the Ultra Ball (x2).