So I tried it in some simulated Cessna, and as I predicted, upon rotating so that my head pointed at the ground, the plane started to descend. I'm a pretty terrible pilot, though :)

I think this has a lot to do with the wing's angle of attack (most planes' wings have a slight upward tilt; when upside-down, that tilt goes downward instead). It would be more interesting to see the effect on something without an AoA bias.