No.
While teams can be based in schools as part of the school day or as an after-school program, many teams are from home school groups, church groups, or just families getting together to do this for their children.
FIRST LEGO League comes with a Team Leader Guide, which is like a teacher's edition for twelve two-hour sessions. While advanced teams will do more, this provides a framework to get you started and be sure you know all the key parts of the program.
FIRST Tech Challenge offers a lot of resources, including a competition manual, robot-building resources, programming resources, and more. Additionally, FIRST Tech Challenge provides a free introductory Robotics Engineering Explorations Curriculum.
FIRST LEGO League Challenge teams should plan on $1200-1400 for the first year, with about half of that being one-time expenses like the robot that will be reused in following years.
FIRST Tech Challenge could cost $4000-6000 for the first year. Teams are expected to put together a business plan and are encouraged to ask for sponsorships from local businesses.