To find out if I have late onset cah, do they test your thyroid?

They should, only. Because this is an endocrine abnormality (endocrinopath) and it is not uncommon that if one has one, that another may co-exist. However, generally, thyroid function and hormone levels are normal with cah.
Part of testing. When someone has symptoms of nccah the thyroid as well as other hormones outside of the adrenal are tested to help establish what the problem is.