it's possible, and you wouldn't want to sand it, anyway. apply deck stripper per product instructions, pressure wash it off. repeat until the stain color has all been lifted. after that, hose it down with oxalic acid (aka "wood brightener") mixed per instructions. let the oxalic acid solution sit on the wood for the recommended amount of time, keeping it wet for the duration. pressure wash the brightener off and let it dry for several days.
the deck stripper should make quick work of a low end product like Thompsons, especially if it's been out in the weather for a couple years already. deck strippers are strong bases (low PH), so treating with acidic wood brightener (high PH) after stripping is very important to raise the PH of the surface to something near neutral. this will help it take new stain or whatever finish you may want to put on it.