Message Inbox does allow you to reply to a message; just check the reply radio button to the left of the incoming message, enter your response in the Reply text: field, and hit submit.

However, it doesn't allow you to send a message to an arbitrary monk/usergroup. To do that, it's much easier to just go to Fullpage Chat than to temporarily enable the chatterbox. (Or if you feel perverse, ad_and_talk.)