No, it does not allow Anonymous monks to chat. You are still forced to post who you are in the real time chat, it just means that your identity is only tied to what you say while it is fresh. Those in the Chat will be able to tie you to what you have said, but it would be harder for anyone to legally tie you to it 1hr later.

As for the technical feasibility, you have to log in to chat. During the chat the system is capturing who you are. A 0 identity bit can also be passed in the post. As the Chat updates with a new post, it checks 10 posts prior ( one that has already scrolled off the screen), and clears the identity if Identity=0.