Also - Groupon spends a ton of cash on Adwords to acquire subscribers. Google can easily just "out bid" those with their own ads for free.
Then again, I do not think Group is concerned about the long-run
Of course, google can put an ad on the homepage. Since they don't sell that inventory, it is about as close to a free lunch as you can get.
Google has promoted their own products on their own sites outside the ad system in the past, but they got a bunch of greif for it. There is a Chrome ad on the homepage today that targets old IE browsers, but that is the only exception I am aware of.