Power consumption is a function of the voltage squared, but maximum operating frequency drops down slower than that as you lower the voltage, up to a point as GP said. So efficiency defined as f*P goes up as V goes down.

People definitely do that, the voltage you chose to power your chip is always a consideration, it's one of the variables used by laptop manufacturers to manage thermals, and it's also pretty common to lower the CPU voltage so that you can run a desktop system with passive cooling.