If Chewbacca crew is on Han Solo MF and I take a Advanced Homing Missile and am dealt the damage card while I am at full shields, can I use the Chewbacca crew to discard the damage card even though I can't recover a shield? Many times I see in this game where I can't do one beneficial action due to not being able to do the ENTIRE beneficial action and I want to make sure I can use Chewbacca crew in this way before I run him. Thanks in advance.

Yes you can.