It will still show up and will probably cause you problems, as in being placed on a hold. However, since prosecution was deffered on both charges you were not charged and convicted. I take it you agreed to do all of the things you stated, which means since you did so the charges were dropped. You will still be able to purchase a firearm, but I guaruntee you will be placed on a hold. You are extremely lucky that the charges against you were dismissed, if I were you I would go buy a lottery ticket.