I don't think this will work. The graphics card is inserted into a socket slot on the motherboard and takes power from the PSU supplying the motherboard via that socket. So the only the secondary power supply to the Graphics card is via the power socket on the GPU. Connecting this to a second independent PSU has the danger of where its voltages are referenced to unless both are referenced to a common rail. I am not sure if this would occur via the GPU itself but I would not dream of risking a blown motherboard/GPU for the sake of getting the correct PSU for what you need to power the computer. A PSU is certainly cheaper than a new motherboard/GPU/Processor.
Good thinking though on your part.