It's within the realm of remotely possible for a GPU driver to take the rest of the machine with it. However, it would be *highly* unlikely. It would require an old and/or poorly made PSU running on the ragged edge of being in spec failing in a very specific way.
Here is how this might happen. Let's assume the driver gets you "30% more performance" by using more of your video card hardware. Wattage used goes up, PSU gets pushed over the edge. 12 volt regulation fails by giving you really, really, REALLY *bad* ripple under full load. Various components hooked up to the PSU die.
So it's (very) remotely possible, but I don't see how a fan failure would cause this. And the driver would at most contribute to the problem, not cause it.