First, welcome to the Wowza forums. Regarding your question, it seems you would like to develop a chat application for iOS.
There is not a way to do client-server communication using Cupertino streaming that I know of. So there is nothing built into Wowza to use this method.
Therefore any chat application that you developed utilizing Cupertino streaming would do the chat portion independent of Wowza, while Wowza would handle the video/audio side. Wowza does have HTTP Providers with which you can do client-server communication. Or you can use anything that Java can do. I see Safari supports HTML5 Web Sockets. Maybe that could be used.
Hope this helps.
(I don't do iOS programming, so forgive me if I've missed something obvious.)