Yes, they get a notification in the middle tab telling them someone left them a message. From there they can continue to chat with you if they would like. Some times however, the notification does not appear. Here is what it looks like when it works properly:
http://www.radphone.info/wp-content/uploads/2010/09/7ab32827021jn1tv.jpg.jpg
Edit* I thought you wrote iPhone and answered specially for the iPhone, the other answererr got it right.