Possibly, but Valve isn't exactly a prolific developer in terms of titles and timeframes. They would not restrict a big budget title the very small marketshare this box would likely have in the first couple of years, and other publishers wouldn't be keen to jump on board when one publisher controls the strings I bet. I would also majorly piss off their Windows gamers, which is their bread and butter and will continue to be so for the foreseeable future.
I'm personally interested in learning about what its UI will be. I doubt it will be Steam full screen, but something different with multimedia features built in. Maybe even Android based.
Big Picture mode gives me promise, they certainly have aptitude in this area. It's not perfect but damn it's impressive for a first showing.