I stand corrected. The client counterpart of such a server-side streaming application could be a Java applet or browser plugin. Full duplex would be required for such an application. Traditionally, with the content-length indicated in requests and responses, many browsers and servers have used a synchronous model, where clients try to submit the whole request, then only after it's complete, begin read the server response.
Many servers operate similarly and read the entire request before starting the reponse.
This is generally true for small GET requests, which the server can afford to buffer. However, for POST, the server will not buffer since that would make the memory footprint of the server very high when multiplied by the number of connections. I have found that HTTP clients typically break if the server tries to respond too early to a request, before it is complete. For example, this can happen with a large POST request to a non-existing object. The server detects early on that the URI doesn't point to a valid object on the server, and will try to respond immediately with a 404 response.