In $dayjob I work for a telco that deploys fiber to the home.  If we are providing voice services over fiber a battery backup is installed (we maintain) that powers the customer's phone in the event of a power outage.  It does not power their router, etc.  99% of the customers do not install a UPS for their router, etc.  We try to explain that to customers, but we still get calls that they can't get on the Internet when their power is out.

So your voice is part of the modem which isn't a router? I assume it uses IP for voice.

Mike