I love my Xbox 360, but no, it's not Web 2.0. For as far as this Web 2.0 concept means anything, it's about open methods of sharing: RSS, API's for web applications, etc.
It's cool that I can download things from the Xbox marketplace, but that's the only place I can download from. Nobody else can put up a marketplace that conforms to some API, that I can now add to my places to download content from.
Same thing goes for the media-center type capabilities. I'm sure its great if you have an Windows Media Center PC. But for me, the only good thing I get is if I plug in my iPod. I can't get anything of value off of my network. Yes, I know about Windows Media Connect, but, as far as I can tell, it's worthless when your content resides on a third file-sharing device not running Windows. I'm a technical person, but I haven't figured out how to get it work with either mapped network drives, nor UNC paths to an authenticated network share.
Xbox 360 has a very impressive walled-in community. Web 2.0 is about communities without those walls.