Google didn't really want to buy spectrum. Schmidt even publicly stated they had no intention to buy the spectrum. They were just after open access to the "C-block" of the spectrum which they got as a stipulation to them making a slightly higher than minimum bid. They got what they wanted, and it wasn't to own the spectrum.

With that said, I don't think google has any real interest in being a carrier, as that isn't where they make their money. They can leverage the mobile network much like the internet and continue to make their truck load of money via targeted ads.