In the EAP you show the ability to navigate and browse Guide articles while waiting to be served.
Thinking myself a chat visitor, I would be hesistant to try this out (i.e. to discover this works).
I would assume that if I hit that Chat button, there is a high probability of the chat ending. Perhaps I associate the 'back' button with the back button on my browser that would often 'undo' things.
I'm not sure what the solution to this would be - but I would like to hear how you think about this one.