It's even smaller than that. Honestly, if it's any more than a half gallon, I'd be surprised. Basically it's a box, about 6"x6"x4" that is directly underneath the feet of the person in the right sight. As for the uninterrupted fuel supply, that is correct, however I wouldn't go so far as to say inverted flight or even prolonged zero-g flight. The fuel line that goes from the reservoir to the auxiliary fuel pump is attached at the bottom of the box, so it still needs gravity for fuel to proceed on through. I tell my students it's for an uninterrupted fuel supply since it is a gravity-fed system, but beyond that, I'm not too sure what the purpose is.
By the way, if you get a chance to pull up the flooring or to see the plane with the carpet pulled up, you'll see it. It would take all of about 30 seconds to pull it up and take a peek on the next preflight.