Nobody would allow people to go through security the night before then leave the airport. Arriving 3 a.m. is too early also. Nobody is around at 3 a.m. including AA staff and the US Preclearance folks who open at 4 a.m.(used to be 4:30). Even at 4 a.m. you are more likely to check in at a kiosk because AA folks are none to prompt at the podiums.
If you are dropped off at 8 p.m. and need to be in the airport at 4 a.m. then stay at the hotel attached to the terminal or the one at the end of the monorail. That's more than 4 hours, it's a proper night at a hotel.