Do you mean disk space? Disk space is pretty cheap, particularly since Xboxes are increasingly storing data like saves and achievements in the cloud rather than on disk.
The Xbox at the moment has a pretty hefty OS memory footprint, but when the (premium, not XNA) game itself is running the entire OS evacuates memory to free up resources for the game, leaving only a lightweight hypervisor behind.
I would be surprised if the OS took up resources like that whilst a game is in use, if for no other reason than it would put a huge and unnecessary strain on the premium games that are running on the platform.
Also it's unlikely that you'll see a C++ version of XNA released. There's not a huge demand from the quick-and-dirty games market to build stuff in C++ when C# is so much more productive (particularly since Xboxes are pretty powerful even at C# when they've got a GPU that big powering it). Obviously premium games tend to be written in C++ and that will undoubtedly continue to be the case with the next Xbox.