No. AA will not check for connections greater than 12 hours. It's a computer says no situation. Can't remember if the cutoff is 11:59 or 12:00, so not only will you have to collect at TPA, you may have to collect at LAX (depending on the exact length of your layover).
You can ask at check-in, and they may be willing to find a way to do it, but I would plan as if the answer will be no.