In my opinion, starting the APU would definitely have helped.
Am I missing something? APU gets you out of ELEC EMER that brings CM2 instruments, it can take over pressurization, main use is starter assisted relight which wasn't going to happen. None of this would change PK8303 fate. Sully started APU from memory as good airmanship to get an engine going but once that didn't happen he also got no other help from APU. It doesn't get you out of G+Y. In PK8303 once they lowered the gear they were done in. Even if they could raise it they would've lost more height.