Are you thinking full-scale FRC, or something more like FTC or VEX?
Team 3180 hosted
a VEX competition this past December where teams learned the game at 8pm and had to play the game by 8a the next day. Although it lacked the glory and mechanics (and headaches) of full-sized FRC robots, it was not at all lacking in teaching design, strategy, and teamwork, and it avoided the inevitable 6-week-burnout that accompanies the FRC season.