Type of routing doesn't make a difference for the above result. The main assumption is that node-pairs that want to communicate have random locations. That leads to O(N) pairs trying to go across O(sqrt(N)) links in the middle.

In practice who knows what kind of communication patterns you would get. Applications would probably evolve around the long distance limit if it existed, but it's hard to imagine not having backbone links. Most likely the meshes would stay relatively localized (and I believe there exist a number of regional wireless mesh networks out there serving real customers).