I've had work book either the night before or a half night early a few times for flights to europe where I'd arrive early and have enough time for a few hours sleep before going to meetings.
I don't think I've ever been charged a fee in the US for checking in a few hours early - either they have some rooms that cleaning is done on or they don't, and depending on where I am in line I might get one. I usually use online check-in when it's available, and check in as I'm boarding my flight. I recently did that for a redeye to the Boston area and when I arrived in Boston the hotel already showed my room as ready at around 7am, so I had time to stop for a quick shower and drop things off before going to my meeting. There was no additional charge on my bill for the early check-in (Springhill Suites).