The nanites have been sucking electricity, in one form or another for years, when "the power gets turned back on" what happens is that they go from suck to blow and it is they who are powering all the random devices within their field of influence.
If the nanites are sucking bio-electricity, static electricity and the odd bolt of lightning as they occurr, it's possible that as long as they are co-operative that they could sustain mans power needs in perpetuity.