Yeah, for games I do, I use the Logitech Marble Mouse. It's a trackball, I use the direction of the ball as my "head". So, I push the ball forward, I should "look" down in the game. If I don't invert, I will "look" up instead.
Mostly, yes. Reasoning is this: I tilt my head back to look up, I tilt my head forward to look forward.
However, some games do make me feel like using a normal mouse. For example, a flight sim where the crosshair is not fixed in the center of the screen, ie, the crosshair moves exactly the same as the mouse pointer in any OS. In this case I am think of moving the mouse to a certain location, and not as a means of controlling my view vector.