Do I still get a turn when my fortress is defeated in a game with three or more players?

Yes. In a free-for-all game of Cloudspire, when your Fortress is pillaged you still take your Turn as normal. Your minions, heroes, and Spires are unaffected by the loss of your Fortress and you still gain rewards for defeating Opposing Units and Spires as normal. In a team game, if any Fortress is defeated that team loses the game.