Does the wheel on the wall do anything at all?

Solution 1:

To my knowledge, it doesn't. As you proceed down the hall, you'll notice other random objects from elsewhere in the game.

The obvious conclusion is that is the narrator's area (the original narrator, not the new one), and that it also represents the futility of your actions in the game (much like everything else in the game).

However, it appears to be left intentionally vague.