Is there a way to automatically turn off registration when full?

Unfortunately no, we don't currently have a way to automatically turn off registration.

However, you can set a size limit for each team, though that is only used for the auto-assignment to teams. People still will be able to register, they just won't be automatically assigned to a team.

You can also put a note about limited registration numbers on the registration form or in the welcome email. Once things start to fill up, you can hide individual age groups from the registration form, and, of course, you can completely turn off the Student and Volunteer public registration forms at any time.