I can think of several disadvantages (though I may be wrong and naive):
1. If you're running a node, and I'm running a node, my data schematics might not be compatible with yours. If I write a uniform backward-compatible RPC, then it'll be a little better.
2. I can't selectively allow you to copy some data (photos) and not others. If you are a user on my database, you can access everything you have permissions to. It's hard to set fine-grained permissions.
3. Push notifications will be hard. I'd have to poll the database for changes.
For that matter, the same can be achieved by putting a giant XML file on Git, and having each person set up a remote, or using a complicated set of shell scripts and rsync. Couch's replication facility is really neat, especially if you want to scale horizontally or if you're adding redundancy, etc.
CouchDB is becoming the new hammer. It'll get tempting to write source control, file backup, etc, using this database because of the data sync, and decent query capabilities. But I feel that building a social network on top of CouchDB's replication might not be the best of ideas.