Lots of the polishes marketed as "guitar polish" are basically silicone, wax and fragarance. They look great, but there's a real problem with them.
Silicone takes something like ten years to dry. That's not much of an exaggeration; silicone simply will not dry. "Not a problem - polish it off".. but it is a problem, because the silicone seeps into the nooks and crannies of that guitar and if it ever needs to be repaired or the finish fixed, you're stuck. Silicone will not take a glue or a finish. So silicone polishes look OK but are the repair professional's nightmare.
If you want to polish it, look for a furniture polish that has no silicone and cleans the finish, or use caranuba wax. I think Pledge is OK, but I'm out of touch with the chemistry thing these days.
If you really need to bring back a finish, the best thing to do is apply successively finer grades of polishing compound. My favorite is Meguiar's Mirror Glaze. It's what pilots and small airlines use to clear the haze off plexiglass windshields in aircraft. But you do not need to "protect" the finish.