We can't account for what an auditor accepts or doesn't. The fact that you haven't been called out for the lack of a documented process at this point doesn't mean you never will be called out. You know the requirement, so it should have been in place at the time of the registration audit.
Training and quizzes might be part of competence evaluation, but not the only part. Many people who are trained and have evinced evidence of knowledge of the requirements will crash and burn when it comes to actually doing audits.
The short answer is "yes," but we come back to the question of competence. It goes one level deeper now though, in that the trainer should be a competent auditor and competent trainer.
thank you
