In my experience, a hotel will check you in if they have a room available and ready. If not, as sometimes happens, they have always stored my luggage for me until check-in time.

It seems to help, when you arrive at the check-in desk, to say something along the lines of "I know I'm early" — for one thing, this means that the check-in person doesn't feel constrained to go into a long-winded explanation of either (a) why there is no room available or (b) that he/she is doing you a favour by checking you in early, but it also seems to make them more disposed to be helpful (I don't know why).