Panels usually run until 3 or 4 in the morning. So there's usually stuff to do. I'll probably take my sewing machine to the lobby tonight after my friends go to bed. (Working 3rd shift has borked my circadian rhythm.)
The hotel really frowns upon people sleeping in areas that aren't a hotel room. If they catch you the first couple of times, they'll probably just wake you up and tell you to go back to your room to sleep. But if they keep catching you, they may ask you to leave entirely.
But if a con-goer catches you (like me, because I'm mean like that), they may snap your picture while you are dead to the world.
As long as you aren't making a big production out of it, you can usually bring outside food with you.
If you must stay at the hotel for 24 hours without getting a room, please, please, please bathe. Even if you're just taking a "trucker's bath" in the bathroom. (Soap up a washcloth and wash your mouth, pits, butt and crotch.) Your fellow con-goers will thank you for not stinking up the place.