Groups will work fine for that purpose, and you can easily have 200 groups.
All you would need to do is to manually or programmatically map the field onto a group. But you might also want to have people send in some kind of "proof’ after registration.
You could do it manually, code that yourself, use Pavilion’s custom wizard plugin for that.
That’s true, but you could have users who want to make it public display that field somewhere else, i.e. have a “private” building field and a “public” building field.