Of course they do. But IME sometimes, if a student or parent wants to test and the coach doesn't think the student is ready - but the student or parent is insistent that they are - the coach may put the student up for the test just to prove to them that they aren't skating at the level they think they are.I don't think a coach would test someone who isn't ready. It may reflect badly on them. They want to have passing students.
IME coaches do this very rarely, because they don't want to waste their own time and the judges' time, but it can happen.