From an anonymity perspective, it is just as secure as current bitcoin protocols. Public anonymity at the sacrifice of privacy. In which case, if your 'twister' info is out there, you can theoretically be identified.
What I want to know is this: What does Bitcoin have to do with this? You can have peer to peer, anonymous, encrypted messaging without any of the nonsense that Bitcoin entails.
What is the point of that ledger? Public keys identify users on their own.
So sure, I can grant people are more comfortable dealing with usernames than with public keys, but that sounds more like a UI problem than a technology problem. People are certainly capable of dealing with Tor hidden service addresses, and I suspect that is because they are already using a UI they know well (their web browser).