In the event of a natural disaster, cell phone service is remarkably resilient if it's not overwhelmed by people calling their relatives to tell them they are alright. That's why SMS texting in a disaster is always almost more reliable than trying to actually call someone.

Cell phone towers typically are built very well, and have sufficient battery/generator backup to keep them running for up to 48 hours after losing main line power. As long as the fiber connection to the shack remains intact (and that conduit is designed to flex quite a bit), cell phone service will be there.

There's also portable "Cell Phone Trucks", that can roll into an area and provide cell phone services in the event of a major disaster as well. These trucks have Satellite uplinks and masts that can provide basic cell phone coverage as well.