Uh, no. At least one of these things is not true.

> It also means other segments of government can never use these messages in any kind of legal proceeding without a prior valid search warrant.

Unless there is a special legal provision applicable to specifically this system, no, it doesn't. That certainly is not a consequence of being an employer-owned, for-official-business-only system of a government agency, in fact, it is the opposite of what that would generally means, which is that it is already government information from the start and law enforcement (federal or state) wouldn't need a warrant to use it against individuals. (This is separate from whatever process might be necessary if the Army preferred not to share it, for security or other instiutional, rather than Fourth Amendment, reasons.)