If you're opening a webpage from the embedded browser in Media Center, it will play through the browser, not Media Center, so you can't play to the Id as a zone that way. However, if you're using File -> Open URL... that will play through Media Center. In that case, you should be able to select the Id as a zone and play to it that way.
As for adding a web browser to Media Center on the Id; I could not give you a definite answer one way or the other. It has been talked about, but I don't know of any immediate plans to embed a browser in Media Center on the Id. You can still access a browser on the Id by selecting the Audio or Video section. On the upper right will be some links in a toolbar, like Amazon, AMG, Google, et cetera. You can access a browser through those links, and even create your own links.