Considering the power consumption, bandwidth, etc., 802.11 Ad-hoc networks might be a great choice for this concept. Plus there's already OLSR[1] for handling multi-hop packets. Unfortunately currently mobile devices are only equipped with one 802.11 adapter and it can be either ad-hoc mode or Wifi-client at one time.
I was talking a little bit about this in a comment down below, but android just added adhoc wifi networking (in v4.1 maybe?) so it's not too widespread. iOS has had it for a while, but the app is currently android only, which seems to be the most appropriate OS for the project anyway.
Either way it'd be great to support it for those power reasons you mention and for how much faster it would be to sync.
The problem is that a wireless (802.11) interface can only join one SSID, and work in one of the modes (ad-hoc, wifi, AP) at one time. If like current phones on which there's only one wireless interface, when people are connected to Wifi, they won't be able to use ad-hoc.
I've been hoping there's a company coming out with a phone/tablet with two 802.11 interfaces, so I can stay on Wifi and at the same time join an ad-hoc network :-)
I'm not exactly sure how the adhoc stuff works on android but there's a specific api for it which is usually used for local gaming. In any case the use case for this app is that the Internet is shut down in your ___location so you probably don't want to connect to it anyway.
I'm not sure how far Android goes to sandbox you, but you might be able to write an app that runs in the background to detect/manage/switch-between network interfaces depending on what the intent of the user is at that moment. It'd be a handy little tool if it worked.
[1] http://www.olsr.org/