Is your router not at the same place at the big white FIOS box?
My router is at the same location as the FIOS box, and with some creativity, you can hook the Verizon provided router up to their little UPS. It is not much, but should be enough to handle a power outage. I don't actually know the specs on it, but when I have a power outage, UPS is generally for me to save my work, and shut down.
What is the VA rating of the UPS you want to connect to the remote location?
If it is large (and expensive), I can see the point (cost wise) in running the NMB cable and plug/receptacles. But if your UPS is only say 550VA, then you're probably wasting your money, since another 550VA is about $70 at Amazon.com.