I think it really depends on your site and how intrusive it is to the user's experience. If there is potential for it to obscure information that the user is trying to read then it's probably going to annoy your user, which is not what you want.
However, this can easily be overcome by including a simple "minimise button" so the user can choose to hide the chat bubble if they want to get it out of the way.
I would suggest you to keep your design as you want it to work but try to ensure it doesn't take up more space than it needs to. Then include a "close" button that upon clicking will minimise the elements so that the user only sees something like a little tab saying "Live Chat". This can then be tucked away in the corner of the page so it doesn't affect the users experience. That way, if they want it later they can just click that to bring the original elements back.