Of course it can. Higher clocks need more voltage, more voltage = more power draw. The increase is not linear, but exponential. Going from 4 GHz to 5+ can easily double the power draw on the FX CPUs. It was the same thing with the Phenom X6 series. Going from the stock ~3 GHz to a good 4,2+ GHz overclock literally doubled the power consumption of the CPU due to the voltage needed.