Not unless the government is the entity doing the banning (or collaborating with Twitter to ban accounts at its request).
If the government ran its own Mastodon instance, then there would be an argument to be made that it couldn't ban users on that Mastodon instance, depending on the nature of that Mastodon instance and what it's used for. But that's not what's happening. The government does not run Twitter in any way; they're simply users of the platform, and the government's ability to use features of the platform (such as the "block" feature) may be limited by existing laws, the same way the government's ability to do other things in life is limited by existing laws.