RTKDCMB
Senior Master
No, the student signs up when they feel they're ready. Its the student who takes the test at his or her own discretion. Of course, just because a student thinks they're ready doesn't mean they are ready and if that's the case than it will show in the test and they wont pass.
That's a very strange way to do things. Color belt student are, by definition, inexperienced in their art and don't really know when they are truly ready to promote. It is an instructors responsibility to determine where each student is in their training because they have the required experience. Can you imagine a medical student who gets to decide when he is ready to treat patients rather than his teacher and what could happen?
I have seen students who were far from ready for testing who thought they were and students who were ready and thought they were not, it is the instructors responsibility to separate the ones who are and the ones who are not. An instructor should not set their students up to fail, they should only be sent for testing if the instructor feels that they will pass, a student can then either confirm the instructors confidence in them of prove him/her wrong.