MCL 762.11 states that the court "without entering a judgment of conviction assign that individual to the status of youthful trainee." Based on this language the assignment is done without a conviction, and so you should be able to get a concealed weapons permit with a HYTA. However, I advise you to consult a local criminal defense attorney as you may have other issues that could interfere with your rights. Convictions for many crimes will not allow you to have the permit. It is better to consult an attorney first.
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You are correct that successful completion of the Holmes Youthful Trainee Act ("HYTA") means you should not "suffer any loss of right or privilege." Here is a link to the applicable statute, MCL 762.14: http://www.legislature.mi.gov/(S(lrynqljb0q3rugble2krih55))/mileg.aspx?page=GetObject&objectname=mcl-762-14. However, local gun boards have many discretionary powers when making their decision, so I would kindly but strongly recommend you retain a local-area CCW/CPL lawyer to represent you at the gun board hearing. I wish you all the best of luck. Warmest regards, Matt Catchick.