Personally I can't imagine this kind of strategy being used, it doesn't seem like Valve's style. Not to mention that their history favours give-aways and promotions over playing 'dirty' (there would no doubt also be a TF2 hat). You also have to remember they probably only control the games they've actually produced in-house.
I agree; I'm being mostly facetious when I say that it would be "smart" of them to do that. They wouldn't.
But it's the sort of thing that Microsoft would do well to think about as they move to lock down the Windows platform in the face of increased competition.
As a company, Microsoft has always been possessed of the peculiar conceit that their users run Windows for its own sake. (Hence their insistence on branding their cell phones 'Windows Phone X'.) They don't seem to understand that Windows hasn't been a consumer brand since the Windows 95 release, and is unlikely to become one again in the future.