Good point EM, I know when I login to my account it's the bane of banes, apart from the invitation to chat on the right of the screen it continually comes up whilst I go about my daily balances and other chores, drives me nuts!!
So, I think it's only for AGL customers, next best option for you is here for your queries.
Oooops, I boobed it seems, nice when your wrong and someone benefits!!
When I follow that link that you have provided in your answer, it just goes to the contact page. Despite checking all the options included, there doesn't seem to be a web chat option. Is there any other link you could provide?