Don't know about AA. I jumpseat on American Eagle every week though and they are usually very good about getting me a seat on the flight, even if there is pax from earlier/later flights trying to get on. No first class though cause they fly the EMB-145 from Chicago to my base.
On US Airways though I have managed to get first class before. We are supposed to purchase first class upgrades but the crew will stick me there if the cabin is full and there is a seat. I have found that the treatment you get greatly depends on the person working that day at the gate. Make sure you are nice to them and don't bother them when they are busy with cancellations, annoyed pax etc... they will get to you.