Basically, to treat a conscious patient you need his/her consent, for an unconscious one you don't, because you're excused for not getting it.

That's really stretching the word "basically". If a patient is unconscious and there's an urgent issue that will cause serious injury if not addressed and it can't wait until the patient regains consciousness and you did not have an opportunity to get consent while the patient was conscious, then you have an argument for not getting consent, but you can't go around treating unconscious patients willy-nilly.