Probably not. By ancient legal tradition, the government's rules do not apply to itself unless it specifically says they do. (This may seem unfair, but if you work out the scenarios, it leads to fewer absurd situations than the alternatives.) Typically governments do make laws like CAN SPAM apply to themselves, and it is almost certainly an oversight that CAN SPAM doesn't.

On the other hand, it's not a very big loophole. You can probably count the government agencies that are likely to send out commercial email on the fingers of one hand. There's the USPS, Amtrak, and it's hard to think of any other plausible ones. (Implausible ones abound: "Planning an invasion? We know you have your choice of nuclear-armed uniformed military services, so when excellence is mandatory, call The United States Marines ...")