Yes, because if there is a low-level ground-loop issue, it will operate between any interconnected components, whether or not they are powered on or off. The "ground loop" voltage differential is conducted through the shield connection of the incoming RF cable from the cable-TV supplier, the outer shield of any RCA cables, the chassis grounds of the TV, the AV receiver, DVD player, subwoofer, etc. and your ground connection of the house wiring, to which every component is also connected through their AC power cords.
Ground loops are frustrating and difficult to track down and are pervasive in their effects on audio and video performance. But all such grounding issues can be resolved with persistence and/or isolation transformers.
