@kie .v (Ian)  I’m not sure about hiding or removing the chat button in this way, there may be a few workarounds but if your goal is to have the chat window open all the time you could setup a workflow/rule that opens it automatically based on a very general rule to popup a message when someone visits the URL to the website that is your main entry point.  This way it will be very obvious that the chat support is there for them waiting.  

Would this help for what you need?