Lol, remember if you have a blackout your connection goes down and mining doesn't do anything.
That isn't always true. I get internet via a cable connection, and have my cable modem and router hooked up to a UPS backup. When the power goes out, I can continue to surf the internet until the UPS backup dies.
Your internet will work during a blackout and give miners a better chance of reconnecting. The most benefit is if your breaker blows where your router is plugged in though.
You could put a cheap wifi remote power switch on your miners and restart them while your away. Which would require a ups on your router. It would be a lot better then a ups for your miners. A extra 5 minutes of mining when the power goes out is never going to be cost effective.