I think I've used an unsolicited chat widget maybe once. What stood out to me was that the entire experience is setup to be a poor one for the user by default. Click a link on the page and the session is lost. Links sent through the chat don't add target=_blank, either; I'd imagine that the percentage of chat sessions terminated by accident is awfully high. In which case, in trying to help, the support rep is merely adding to the user's frustration.

And that's ignoring the users who get frustrated with the giant, in-your-face pop up. At least they don't have sound. Yet.