No. Shutting off parts of the Internet wouldn't put even a tiny dent in cybercrime. There are, however, circumstances in which it might save people's lives, particularly people who rely on continuously available electricity to live.
For patients requiring treaments to stay alive, there are generators at every hospital and ambulances to pick up patients in dire need. Even taking your ludicrous scenario of total US power outage attack at face value...oil will still continue to burn without the internet. :D