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.
Another benefit is most of the nice ones will smooth out and clean the electricity for you, along with giving you 5 minutes of extra uptime. The uptime is also nice if you have to rearrange wiring for some reason. There are benefits, but it's not going to keep you going when the electricity is "truly out".