Generally your safe. since a 120v to 12v wall transformer is pretty simple the router has an internal regulator. Since 120v power can fluctuate, say from 100v to 130v your input at the router can be from 11v to 13v. usually there is a 5v regulator inside anyway. If you ant to be extra safe get a 12.5 or 13v zener diode and put across your 12v cord to prevent anything higher from getting through (say if you were to run a car alternator to charge your battery where you could hit 14.whatever volts.)

AT&T bought our local phone company a few years ago so the land line ceased to stay alive for very long when power was out and wasn't very relaible when there was power so we swiched to an all in one cable bundle. I've used the power companies web site to verify outage maps and report my power was out.