It won't be higher since the voltage is the same. P=VI. So with same current from battery, higher voltage means higher consumption. I do believe power loss will b  higher though since higher frequency, means more switching operation in transistor, means more power loss. Just my understanding. Haven't study computer architecture, not sure

hehe flawed

anyway, like mengsuan explained, frequency plays a major role in power consumption

thats y i always say, Under clock save you more power than Under volt