Well sure, if it has a 6-pin power input then it needs a 6-pin power imput.
Yes, it makes sense, but I think some cards with auxiliary power connectors will work even without any power connected to it - at least at a low working load (e.g. booting, Windows' desktop).
I seem to remember my Radeon X800XT AGP (on another PC) worked ok without its Molex power connected (not while running Crysis, of course
(Also, double check that you have the GT model and not the GTX or S
From the card S/N, model is GT. And it has a 6-pin connector for sure.