...so It is safe to assume...
thats a HUGE assumption... even if the 18a on the 12v rail can sustain an 8800GT, the card itself probably won't fit. You also need a 6 pin power connector.
I would say you probably fail on at least one of those three points, and an 8600GT would be the smartest choice.
Compact, low power consumption, and no external power connector.