No, it most certainly does not.
Individuals in the government,
sometimes have free speech rights, but "the government" is not an entity with sentience and cannot have an opinion of its own, other than to support its laws and principles. It can only support and defend freedom of speech (in the US, anyway), not comment on the speech because commenting on the speech is making official policy
establishing or de-establishing the legitimacy of that speech. I bolded "establishing" because the issue gets clearer to people when dealing with the religious establishment clause of the 1st Amendment. This is true at all levels of government, including me, when I was a deck seaman in the Navy.
Example: The Chief Justice of the Alabama Supreme Court was fired for putting a big monument to the Ten Commandments in the courthouse.
http://en.wikipedia.org/wiki/Roy_Moore
This act, as an official representative of the Alabama state government establishes religious principles as being The officially recognized religious principles in Alabama and thus violates the Establishment Clause. His opinion, expressed in an official capacity, is not legally permitted.
Following the issue with the anti-Islam video, US government officials, including embassy websites and the Secretary of State made multiple statements against the video and even went so far as to run TV ads in Pakistan denouncing it. In addition, the government petitioned Youtube to re-check if the video should be banned and sent the FBI and local police after the maker of the video (if anyone is unaware of these facts, I can source them). Since the speech in question was religious in nature, this, imo, violates the Free Speech Clause and the Establishment Clause and perhaps even the Free Exercise Clause, since the maker of the video probably made it because of his own beliefs.