Getting here late, but yes, you do want to have the locker drain overboard, and not into the bilge, since it is pretty darn difficult to seal the locker from rain water.
As for the Starboard, it can not be bonded (think polyethylene milk jug). But while it can be welded, I can't imagine it would be worth the trouble. Just use marine grade plywood, cover it with glass, and paint it over. Then put a mat over the bottom to protect the surface from scratches from the ground tackle.