Keeping the silicon cool reduces power consumption by about 3.5-4% per 10K.

But that should not be case for idle, so lower fan speeds (or no fan) seems logical

This is correct. Lower power consumption as a result of better TIM and thus lower core temperatures:

http://en.wikipedia.org/wiki/Poole–Frenkel_effect

https://forums.anandtech.com/threads/effect-of-temperature-o...

The effect is so pronounced that a watercooled computer running under full load will typically use less power than an identical aircooled computer, because the lowered silicon current leakage more than makes up for the power consumption of the pump and additional fans.