I would assume not, but they do have some kind of problem with processing aether. Not only can they not use it, it actually seems like they might have less of it than the other races. Take Nero during his little trip through the void as an example. His reaction to having his aether sapped was much worse than everyone else's.
In any event, we don't actually know how reincarnation works for Ancient souls. For all we know, they could always reincarnate as the same race they were shattered into in a given shard. E.g. a hyur would always be a hyur, an elezen would always be an elezen. The only thing we know at this time (and really, I suppose even what we think we "know" is just conjecture with a lot of supporting circumstantial evidence) is that these soul fragments are not dissolved in the lifestream like normal souls.
