Facebook messages work fine with an input box at the bottom and the conversation continues to scroll if the person you are speaking with is typing. Even old school chat rooms generally had the input box at the bottom with the messages continuing to float up. Perhaps it just becomes a user option on whether the messages should auto-appear or not.
Perhaps it would detect if you are replying at the very bottom of a topic, or inline to a previous reply. If I am replying inline to someone’s reply, then it wouldn’t scroll. If I’m at the very bottom of the thread, then yes, continue loading new replies as they come in.