Peanut allergies are a disqualifying variable in military processing. I myself was DQed for a peanut allergy, went for a medical waiver via an allergist, got several blood tests, and two different points of view on my case. It was stated to be a mild condition. I heard back from the DOD, and i was permanently disqualified after two months of waiting.
If i were you, if the allergy is not that severe, you should keep the allergy under the sheets.
Hope he has more luck than I'm having with the military. I've been turned down for the Marines and Army for a medical disorder, one I don't want to disclose for fear of shooting myself in the foot (tried to get a waiver with the Army and still got turned down). I'm currently trying for the ANG, which has changed its med standards.
Good luck to him. And if your son doensn't get in, he can come to me if he needs someone to talk to about it.