You will be able to check your bags all the way through to the final destination. After you clear immigration, collect your bags, clear customs, then drop off your bags for the connection. You can do this even if the connection is on another PNR. Just make sure you give both PNRs when you check in.
TBIT is right next door to the AA terminal (T-4). Depending on your arrival time, plan a minimum of 1.5 hours, which is risky. I'd go more like 2.5. If you have to fly AE, add 20 minutes more to get to the satellite terminal.