The answer is, yes. Some yeast die, new yeast are created, yeast split to make other yeast, so the new yeast is a "clone" of sorts of the sister yeast. This is what they are doing when you make a starter.
Yeast mutate because of what we do to it, for instance since you are harvesting from your kegs, you are selecting only the least flocculant yeast in the batch, so eventually you may have trouble clearing the beer, but maybe not. Yeast are awesome warriors and have a will that we cannot crush, they are my hero friends.
I've never harvested from the keg, I probably will now since my juniper yeast appears to be extremely flocculant, . . . . and, the fact that I harvest alot.