My impression was that keybase is distributed? Can it be used without talking to keybase's servers?
Keybase offers decentralized trust, in that the Keybase server can't lie to you about someone's keys -- your Keybase client will trust their public proofs and not the Keybase server -- but it's not a distributed/decentralized service as a whole, because you still receive hints from the server about where proofs live, and learn Keybase usernames from it.
(I work at Keybase.)
No, I don't think the tech is quite there yet. Even just handing out human-readable usernames requires blockchain-style consensus, and we don't have a blockchain being followed along by everyone's machines to adjudicate consensus requests (yet!).
The folks at Blockstack Labs are doing fine work in this area, though: https://blockstack.org/