Should I seal around the base of a bath/shower?
I would caulk any joint between fiberglass and tile. Some pre-made fiberglass kits have ways to overlap and seal the joint, but that doesn't appear to be your situation. Water coming out of the shower will be much more significant than any moisture that makes it through the tiles and grout.

That said, if moisture eventually deteriorates the walls and tiles, the best option is to replace the wall and then use a waterproof membrane that prevents any moisture from getting to the wall.