Verizon had their portable cell towers up during the California wildfires. They have a robust network and are very aware of how critical cellular communication will be following a large scale disaster.
I have no doubt a major disaster would put landlines out of commission for quite a while. Cellular traffic will skyrocket but SMS texting will probably still go through faster than making voice calls. Being able to text family and friends in a disaster zone may be the only reliable method of communication for the critical first 72 hours.