I checked in a few times at 7am and there wasn't a problem at all.
It would helpful to call the hotel the night before and they will know how many rooms are still available, hence, if they are available then you can have one at 7am! They will make a note of your early checkin. Also, get the CSR's name.

It also helps to be Elite as I checked in once at 10am and the person next to me was told the room won't be available till 3pm...another benifit to be an elite -- i guess!