I concur. Early check in is usually early AM, 2 hours early is really not that early, and it would be unusual for a hotel not to have a room ready.
That said, RI's have different types of rooms, if you booked one of the type rooms that they have very few of, and they are all occupied and everyone waits until the last minute, then of course you might not get it.
However, I'd be 99.9% chance you get right in at 1PM, especially if you let the hotel know that morning.
Billy