> In one of my computer engineering classes, I learned that power consumption rises as the square of clock frequency - so doubling the clock will quadruple the power.

This is not quite correct. Switching power of a chip (ignoring static leakage) is proportional to voltage squared times frequency. Most chips require a higher voltage to reach higher clock speeds, so there is a quadratic relationship there. However, I believe that the raspberry pi does not have dynamic voltage control, so reducing clock speed without also reducing voltage will not effect total switching energy consumption.