Not the full BlockChain with all of the data that goes with it.  Each client would only cache the data that they and people in their area are using.  If it resulted in free wifi access everywhere, free Internet, phone, music, etc, that might be the killer app that brings people in.

In fact, is someone created an altcoin that did this (just transferring small amounts of encrypted data around for free or extremely cheap), that would be killer app enough for that client.