However, just for perspective, on a dual channel ILS or GLS, with TOGA to LNAV, the A/P will remain engaged for the missed. I would assume AA's 738's have this capability.
Actually, none of AA's 738s have the dual channel certification... single channel only for all operations. That is why a CAT 3 is hand flown using the HUD. So our A/Ps still kick off in TOGA even on a coupled CAT 1 ILS.