Have you looked into "Live anywhere"? Its what I believe is the beginning of what your talking about. My Xbox Live gamertag is linked to my "MSN Spaces" blog and gets updated as and when I play, this is the start. Eventually I do believe that MS will indeed allow cross platform gaming. I imagine the PC players will always win versus competitions as I would argue that they are more "hardcore" gamers, but it will be frickin fun all the same!
It will also be a good tool for Microsoft to get people to buy more 360's.