^^^ It's long been implied in trek that an Admiralty means "no command of a ship", and on-screen dialog supports this. In Wrath of Khan, Spock admonishes Kirk that it was a mistake for him to accept promotion and that command of a starship was his "first, best destiny". In Generations, Kirk tells Picard never to accept a promotion and always remain in command of a ship.
Then again, their are also on-screen exceptions. In both Borg incursions into Federation space, Admirals were in command of ships that flagged larger battle groups.
During WWII, Admirals did command ships, but they were always flagships of battle groups and task forces - it's probably considered a purely wartime TDY posting, as it appears to be in Trek. I don't know if they still do it today with our carrier fleets. I'm inclined to say it is a super-rarity, if it's even done at all any more.