[Carl n Susan]

If the full tank is the galley one controlled by the handle near the wheels and the less full one is the shower tank controlled by the lever in the convenience center, then the answer is a qualified Yes.

The galley tank is physically higher than the shower tank. Consequently, if you open the valves for both tanks, with the drain valve capped!!!, then the upper tank will flow into the lower one. You do want to be careful to NOT overfill the lower tank as they are prone to popping their lid, due to the water pressure, and leaking.