Does mining require a power source when I'm not looking?

In KSP vessels don't seem to consume or gain any power when they aren't loaded. So, for instance, a ship with no power generation can fly indefinitely without losing electric charge, as long as you're observing it from the tracking station or another distant ship.

Does this also apply to mining operations? More specifically, will my mining base mine at full efficiency (even if the base consumes more power than it gains), if the base isn't within loading distance?

Your mining base is also considered a vessel and will not consume power when not loaded. The mining base will then continue to mine ore for you while you do other missions or while you are on another screen.

The drill continues to operate just like how the survey scanner continues to operate when not loaded.

The mining base, however, does not convert the ore into fuel and oxidizer until the ore tank is full.