I suppose it might depend on how finicky you want to be. If money is any object, I doubt the K series pays off for you .vs. buying a processor where power-savings is a built-in optimization, at some loss of ultimate performance - which you'll be losing anyway with underclocking. The first "K" processor to show up in cpubenchmark's power/performance chart is a LONG way down the list.
Most serious power-savings-nerds in the NAS arena use an Atom, from what I have seen. On my 24/7 router builds I opted for (pre-haswell) i5-3470 on bang for buck while still having bang - those systems typically use (measured) 30-50W to run (500W bronze power supply, 3 fans running with MB speed control, full size case.) Plenty of folks use an Atom in that job, too - for me, that's "low enough" and leaves headroom for some things I want my router/firewall to have headroom for.
I decided I wanted to use ZFS for my (bsd-ish) NAS and also that I wanted to spend a bit less on the box, at least for the first try at it, so I got an old rack server for cheap. It's noisy and hot, running around 100 watts (two xeon processors and those obnoxious 1-U server fans, which are noisy powerhogs themselves) However, most of the time it uses 7-8W - it's Wake-On-Lan capable, and when it's asleep, that all it draws.
If you are not using ZFS, an Atom appears to be more than sufficient, and some folks are managing limited ZFS deployments with them (with some of the more drastic ZFS processing/memory hogs, eg prefetch, turned off.)