Can I connect one end of an in wall wire to an electrical plug?
The best bet is to install an inlet where you're transitioning from cord to fixed wiring.  You don't want to run flexible cords through walls/ceilings, so you'll want to find a way to avoid that. 



So you'll end up with something as follows:

Surge protector -> male end plug -> cord -> female end -> inlet -> fixed wiring -> receptacle where projector can plug in.