From the article:

"Most mesh networks are connected to the public Internet, but if that connection goes down, the local mesh continues to work. In Red Hook that means that you could make voice calls (over IP) from your housing project to the local hardware store to see if its open. Or you could email a friend who lives in the neighborhood."

I don't know VOIP very well so this may certainly be possible, but I very much doubt that without an external internet connection you'd be able to email anyone.