Just tried it today also and experience is not good.
1) There is no indicator for me or the agent typing.
When I entered chat, I was typing my questions for about 15 seconds and the agent send, I assume a canned message, saying that they didn't hear anything from me and do I still want to continue to chat.
I copied what I typed before sending a "Yes, I do" , but I can see someone will be frustrated if they were cut off before they finished typing their question.
2) It took almost like 15 minutes of interaction and at the end for the agent still having to send the request to the account services team for an answer. Like what whynotnow said, I prefer to spent a message and go on my way while the request is being processed.