Would the console necessarily run Linux? I see no technical reason for it to not run Windows for backward compatibility and just launch Steam full-screen on boot.
Microsoft might throw up some licensing barriers to that, which strikes me as the only real reason to put Linux on these things.
There's also the part part where Valve would have to pay Microsoft to license Windows. With Linux, they wouldn't have to. Of course, Valve really hates Microsoft as of late, so you can't forget that.
The console could be $100 cheaper by not running Linux. Plus, I'd much rather see it running on Linux and OpenGL. Besides, Valve seems to want to become less dependent on Microsoft, not more, so making a Windows PC/console makes very little sense to me.