Is it possible to cover a ceramic tile bathtub wall with a fiberglass (or even something else) without having to remove the tile or cover the bathtub. The bathtub is in perfect condition, but the dry heat of desert summers is death on grout?

I don't know how bad the grout is , but you can always try to clean the grout and then seal it.
as for other options with covering the tile, most will need the tile removed, all I can think of would be to use cultured marble slabs, these get liquid nails on the back and set in place, set the back wall first and the too sides walls next,
you'll need to cut some 2x4s for braces will the liquid nails drys,
you be left with a few joints that we use 100% silicone

Gosh, I would never attempt to cover over grout that is already compromised. Be safe. NOT sorry. Remove tiles... a good hardibacker in place & know you've done it right.