the answer is kinda yes and no in that the way rogaine works is by making hair grow but it doesn't know head hair from body hair, but it doesn't necessarily cause significant body hair growth growth on everyone though
if you ever wondered why women get the 2% solution and men get 5% is because women are usually more receptive to minoxidil and also of this hairiness is more of a problem with women
the problem is when you apply it inevitably it will get into your bloodstream and grow the other hair on your body
as far as the acne goes, i have personally found i have less acne on my scalp when i started minoxidil but i don't know about anyone else
saying that i don't want to discourage you from rogaine
if you find yourself with excessive hairiness you can either
1)use less minoxidil, unfortunately this also means less beneficial results
2)hair removal cream, the hairiness will be manageable, it won't turn you into chewbacca we call it veet in the uk idk what it's called in the us, i would opt for the "sensitive skin" one though
saying that not everyone has noticeable hairiness on minoxidil