This is a tricky question, as it would depend on the power supply unit (PSU) in question. If it were a generic, non-branded PSU, I would suggest to not hook the GEFORCE GTX 680 up to it. If it were a branded PSU by a company such as Corsair for example, then you should be fine.
If we look at our review of the reference GTX 680, it has a 3D Mark 11 load consumption of 456W. But, a generic 500W might not actually provide 500W of power, it might only provide 400, 420, or 440W of actual power. My advice would be to check the brand, and if its a relatively unknown brand - use caution.
If the 500W PSU you have is an unknown brand, or a cheaper model, I'm not saying it won't work, as it might. But, I would suggest going for either a lower-end card with less power requirements (such as a GTX 660 Ti). My better suggestion would be to pick up a Corsair-branded PSU, or similar, when you purchase the GTX 680 GPU.