Sorry to sound cynical but if its such a big deal at school that he helps himself to food then why is the teacher leaving it where he can get to it? Surely rather than punish him it would be a lot easier to put it in a cupboard and lock it, know for sure my kids would snap up the opportunity of some forbidden chocolate (as would I!). Same at home, only leave out what you want him to eat, leave a bowl of fruit out and keep treats hidden away or just don't buy them in the first place.
Once you've eliminated any medical cause, don't worry about him eating constantly, some kids do just snack all day, just concentrate on it being the right kind of food