Unless a user knows how to turn it off, they are automatically signed in it seems. Many probably don't even know they can turn it off.
I'm on my ipad now and, unless it has been disabled again, I don't even see the Chat box. That may mean that I am signed on and couldn't sign off if I tried.
By the way, I did browse through the chat the other day and saw all the anti-chat bashing. You all have better things to do in there, right?