Not directly. Google is bound by the statutes enforced by the federal and state governments who are empowered by the Constitution to govern. That is why Google can censor its index to clear it of things it does not like, if it so desired. Additionally, it could establish that the official religion of Google is from here forth Pastafarianism and while that might run afoul of some workplace regulations in certain jurisdictions, there is nothing in the Constitution that prevents Google from doing so.