Does CPU clock rate effect battery life:
Yes, reducing the clock speed will give considerable improvement in the battery perfomance of a mobile.
The CPU power is directly propotional to the clock frequency of the CPU. Actually in Mobile phones there are no clock management for the CPU, so it will run at full speed for all the functions.
However in your PC it has a clock management which make the CPU to function according to the needs, which saves power a lot.
Power usage of CPU having dynamic frequency scaling support (Pcpu) is directly proportional to the frequency (f) and the square of the voltage (V):
Pcpu ∝ f * V 2
So scaling in the CPU performance (under clocking) will definitely improve the batter performance.