The only places I am aware of AA enforcing a bag check time limit on the day of travel are FLL and LGA, both of which have limited space and heavy volume. Elsewhere, you should be able to check luggage on the day of travel when the counter opens.
There is no requirement that you physically remain at the airport nor could AA even know that you are on airport grounds even if it cared. Your sole obligation having checked in and checked luggage is to be at the departure gate no later than T-15.