The security lines open at 0330, but I'm pretty sure that Clear doesn't open until 0430. However, with PreCheck, you shouldn't need much time at all, especially in Terminal B (the terminal AA uses). Arriving at 0400 should give you time to get to the gate before boarding starts.
ETA: you inquired how large/busy the airport is -- Terminal B has (I think) 10 gates, so you can comfortably walk from security to any of them in no more than 2-3 minutes, even at a leisurely pace.