They could, but not with the Poorboys
line, of course. They'd likely have either Meguiar's Mirror Shine line, 3M, AutoMagic or their "house" line. Also, they may have only 32 oz. or gallon sizes, which would be likely too big for a typical "weekend warrior."
As mentioned, you likely need to polish out the oxidation to get down to the "good" paint. By hand, you likely wouldn't get very good results if you tried compounding. A good chemical cleaner could be a good start. Mothers Step 1 PreWax Cleaner would help remove oxidation without taking much paint off, and it's widely available at many parts stores and depatment stores.
Without seeing the paint, it's hard to say how much paint is left. Also, (unfortunately) it is possible that your paint is shot and that even after polishing, you may get oxidation re-appearing in a short while. That said, polishing will help stave off the oxidation longer than just waxing.
As well, be prepared to have an uneven looking surface unless you do a thorough job. You may see your rubbing pattern appear through shiny and less shiny patches where you rubbed the oxidation off more thoroughly and less thoroughly. It may take repeated applications to get it looking uniform. Try 1 section at a time to see just what it will take (and how long) so you can use that knowledge for the rest of the vehicle. Try just a front fender first (or the roof, if you wanted to work on an area that wouldn't be seen much).