They did indeed! In fact, mightyena are themselves descendants from the same common ancestor as growlithe, lillipup, and so forth.
I could go further into detail as to when, roughly, each species diverged, but this may overcomplicate matters a bit. The important thing to know is that, indeed, mightyena is very closely related to the “dog” pokémon—possibly, even, to the point where a proto-mightyena might have been the common ancestor and that human domestication led to dog-like pokémon adapting into their own species.
It’s actually quite interesting to look at, actually. Each of the dog-like species share similar traits, but it’s very easy to tell why they were domesticated based on what types they’ve become. But that’s neither here nor there, I suppose.