I think you can accomplish this with a couple of other settings.
You will still need to create a Text chat channel that enables Threading for the Live room to use. BUT you can then turn off the “Automatically add users” option on that text chat.
Then using a Theme Component like Navigation Menu Display Control, you can turn OFF the visibility of the Chat Rooms for non-Staff users: Navigation (sidebar) menu display control
We do this, and then we create explicit links in the left nav for whichever channels/chats we DO want the users to see.