Wattage for my graphics card

First of all, I plug in my graphics card in a different manner than most of you folks; I do not own a desktop, my gpu piece is connected externally through my laptop's express slot. To do this, I use a special unit to creation connection between my desktop gpu and my laptop. The external graphics card requires a separate power supply. My gtx 560 se uses a 350 watt powersupply to function under this circumstances, though the minimum requirement is not certain for me. I overheard that a single gpu unit (without desktop components) can function at about 300w +/- , so I wonder if I get a gtx 680, without plugging it to a desktop, can it function under my 350w power supply?