There's no reason a mesh network can't use an internet connection as a transport when it's available. Moreover a P2P capable mesh can even make use of a central

There's no reason a mesh network can't use an internet connection as a transport when it's available. Moreover a P2P capable mesh can even make use of a centralized server in such scenarios. At the end of the day it's "just" a message routing and delivery problem. When I enable WiFi calling on my phone that doesn't preclude it connecting to a cell tower.