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Are you basing this on the ANO application or a different conversation? It is interesting but I think you have made a leap somewhere that I am not seeing. Or, it just occurred to me that this is something that you are considering. In that case, one piece of that network would have to be able to bridge to the internet. One phone with a data plan may do it. This is really dependent on the mesh network implementation you are wanting to use. What I am proposing isn't a mesh network, just a way to move data from your network to the Factom blockchain that lives on the internet.
Now that we are thinking on these terms... It wouldn't have to be a straight connection. It could be over SMS. There are even network over HAM radio projects out there. That is the kind of abstract thing I was referring to when I said relay. This is the kind of thing I would like to have the ANO funding for. I have no commercial reason to attach this to a HAM radio, but it would be interesting and I may have to buy a ham radio, which isn't going to happen on its own. (Wives only put up with so much...:) ). SMS would happen first and I can already think of a couple ways to leverage that for a mobile network.