It is High School baseball. It is an extra curricular activity on par with the Band or Chess Club. Would anyone be wringing their hands over the "messages" being sent there? If you would then I suppose you can here as well. We do love to significantly overstate the value of sports and the lessons they impart.
IMO it would require a felony or violence committed against another person to stop anyone from trying out. Any other rationale would be capricious and grounds for AD and coach to be dismissed.
Judgement of keeping player should be limited to on field performance and how the player interacts with teammates i.e. is not disruptive. If he can play and is a functioning part of the unit - he should be on the team regardless of when he shows up to tryout.