Upvote:2
I do not know whether DTW will let you stay inside security overnight. Some airports sweep and close the secure area after the last flight departs; others effectively stay open 24 hours.
You can check in for an American Airlines domestic flight at 24 hours prior to departure. If you have a smart phone, you can display your boarding pass on your phone as soon as you check in. You cannot check luggage more than about 4 hours prior to departure.
Most airlines will not allow you to stand by for a flight the night before. American has a same day flight change, but I think the limit is 6 hours earlier or later so I don't think that will help you get out the night before.