Intuitively, I would think that they are. But perhaps there are additional dynamics involved that can lead to slightly off-center holes.
The reason I ask is that, when I apply a center drill to a rotating workpiece in the lathe, I always notice the tip of the drill jumps up a bit, as if it is finding it's own center. Of course, that indicates a degree of "slop" in my tailstock barrel (more than I like). But even the most precisely made lathe will have some tolerances, including in the tailstock. And perhaps that slop a good thing, if indeed the center drill "finds" it's own center; otherwise, an overly-rigid tailstock barrel would try to force the drill to cut an eccentric hole.
I also recall reading that tailstocks are typically made to be slightly above spindle center (to allow for wear and settling-in I suppose). If so, that would further suggest that the center drill naturally finds its own center. It would also suggest that the tailstock tolerances are designed to allow this self-alignment. If so, just how much tolerance should a tailstock have?