Although the subject matter is different, GitTorrent [1] actually uses techniques you propose, by using BEP 44 to store Git revisions in the Bittorrent Mainline DHT, and Bitcoin to store cryptographically-signed usernames in the Bitcoin Blockchain.
You can look at how that implementation was done and what issues they encountered to see what it would take to implement a distributed [something], where that [something] in your case is a social network.
You can look at how that implementation was done and what issues they encountered to see what it would take to implement a distributed [something], where that [something] in your case is a social network.
[1] https://github.com/cjb/GitTorrent