I'd be surprised if the big countries used plain Tor for their vital communication. They would be having their own secret networks or tunnel through Tor. Small countries have probably simply given up hiding their intelligence from the big ones at this point and are simply interested in ensuring their immediate rivals are kept out, which Tor can probably do.
A custom protocol can potentially be fingerprinted. I wouldn't be surprised if they used something less sophisticated. Like (encrypted) direct messages on twitter/reddit/facebook. This way the traffic blends with the rest.
An application level protocol implemented on top of HTTPS can be fingerprinted. If you look up "Website Traffic Fingerprinting" you will see what I mean. That traffic is encrypted.
For official operations, they would not be using the internet in any way, but their own parallel enterprise networks. Tor could be useful for covert operatives, and for generally weakening the grip of governments where we are inducing "popular" uprisings.
