I've had relatively good success checking into a hotel to leave my things after a Monday morning flight, but it's usually just to drop off my stuff, not to stay and sleep.

If the hotel had empty rooms from the night before, and you didn't expect a cleaning during the day, it don;t see how it hurts to check-in early. But sleeping for a few hours then expecting housecleaning while you're out would be a bit much, IMHO.