If the company president is available enough to the employees to receive suggestions and actually act on them then going through an audit does not prove anything. As far as showing that he understands what people do, even an auditor would find it difficult to say they understand a specific job just because they do an occasional audit of it. Collecting garbage for one sunny spring day does not give you an idea of what the job is like day in and day out.
I worked for a division vice president who was convinced he could relate to the employees by attending one of their improvement team meetings. What really happened was that when he spoke, they listened and did what he said. In discussing the event, he did not realize that his "examples" of how they could solve the problem were the only possibilities they considered. As I noted to him: When he talks, they consider him the CEO first and always. My vote is that it probably is not a useful activity for the CEO and the employees will not be as likely to freely express their comments during the audit.
Bill Pflanz