Faster CPU means higher battery consumption?
Yes you're correct. Android will use CPU frequency as required including deep sleep to highest CPU frequency. If Android uses 1.2Ghz for high end task it will consume more battery but on the other hand will finish the task quicker than 1Ghz.

Many custom ROM also allows you to change this CPU scaling behavior by changing the governor. For eg: if you choose governor for high performance then Android will try to scale CPU to higher frequency.