ANSWER: Most of the time.
When cell phone towers experience power outages, for example during hurricanes, they don’t go offline due to the FCC mandate that requires cell phone carriers to provide backup battery power to their cell phone towers.
The backup battery usually only last four hours tops. Some towers in critical areas have electric generators that will run for days providing some stability to the network in natural disasters.
However, if the tower is physically damaged, cell phones are able to find the next available tower. That said, as long as there are working towers in your area that are not physically damaged, you should be able to make a phone call.