Hi Ashley,
Actually, the ID connection status is indicated by a small blue dot on the Host icon. If the dot is, well, blue it means the connection is live and well. A grey dot means the Host cannot connect to an intermediary server (whatever is set - public or private, in the Settings).
But if you just need information about the server on that tooltip as well, I think it might possible to add. I will send this suggestion over to our development.
Thanks.