I don't know that it's skewing the polls, but people not answering the phone at the dinner hour might be. Drives me crazy.
In 18 years in the business I've personally commissioned over 7000 cellular telephone sites in 49 states and 16 countries. Every single site I commissioned had large backup battery arrays installed which will keep the site on the air for several hours (usually 6-10 hours) in the event of a power interruption. About 70% of the cells I've commissioned, and all mobile telephone switching offices (MTSO's) I've worked in or installed, also had automatic backup generators on site. The remaining 30% or so of the cells I've commissioned had the capability of being powered by portable backup generators, i.e., a generator transfer switch installed, to allow for portable generator backup in the event of extended power failures.
The problem with power outages and cell system failure, by and large, is more closely related to the land line phone company and their inability to provide line power to their T-1 repeaters, which feed voice and data to remote cell sites. Remote cells use either phone company provided T-1 or cell carrier owned terrestrial microwave to deliver voice and data to the remote transmission sites. Usually, a microwave fed site will stay up during a power failure and a T-1 fed site will go off air. This assumes, of course, that the cell carrier performs routine maintenance to keep the backup systems functioning properly.