I don't know as I don't have any cards except for my graphics card.
However, I'd expect it to draw something, even when idle.
Have you tried your 5770 using each of the 6-pin connectors in turn? Also, have you tried it in both slots 1 & 2?
I'll be testing this tomorrow with the 5870. I think it makes a bit more sense since its so close to the gtx680 in terms of power requirements.
And yes, I'd expect the expansion card to draw some power as well....i'm using a mouse off of that USB port at the moment, yet it still shows at 0w. strange