Yes, there are ways to qualify without school or state testing for both CTD and CTY. The school is not likely to care about the CTD classes if they don't see the child as gifted.

Does your school do gifted testing or identification? Do you have state testing from the school? Many schools around us don't do GT testing until 3rd grade. If your child is younger the school may not have a program in place even if you can get the ID. My dd6 is in 1st and they don't have much to offer her. The math "enrichment" is a joke and the highest reading group is below her level. We are asking for more, but I'm aware it is unlikely to be much until 3rd grade. Our school is well aware of CTD. They won't consider enrichment classes a sign of Giftedness. They do however recommend it as a place to skip ahead in the Honors track later in middle school and high school.

Are you trying to use the classes as evidence to the school?