My daughter has anaphylaxis to peanuts. She's been attending overnight camp since she was 7 years old, sometimes for up to a month (and to Girl Scout camps, which she loved!). When she was 16, she traveled with a youth program to Israel, and at 17 she traveled by herself to Paris to study abroad. We have never had a problem at any of the camps or programs she attended. If the camp is accredited, they will take your camper's physical needs very seriously and will have appropriate dietary and health staff available. The only down side was that some camps were so concerned about the nut allergy, they made her eat in a separate clean area by herself with a counselor (the GS camps were especially careful about this). She missed being with the other kids for meals, but it was such a small portion of the day, and she knew it was for her safety, so it didn't matter much to her.
The only problem we ever had occurred on the Israel trip, where she had an accidental exposure when they stayed overnight in a Bedouin camp. The staff had made sure that her entire group was peanut free for the entire trip, but other groups weren't. The Bedouin's had served a dessert made with peanuts the night before to the other groups, and as near as she could guess, breakfast pastries served the next morning were probably served on the same platters that the dessert had been on the night before. So, out came the epipen, and she and her counselor took a cab (fastest way in the middle of the desert!) to the nearest ER. By the time they left the ER, the counselor was physically and emotionally exhausted, but my DH was raring to go and asked to go shopping! That's m'girl! :-)
Anyway, try not to worry too much. Speak to the camp director and health staff about your son's needs and the importance of knowing exactly what's in every food he eats. Let them know that they will absolutely have to check every label and make some alterations, if necessary. Food allergies are perceived to be on the rise (only partly true -- more people think they have allergies, but testing proves otherwise), so more public institutions are becoming more and more cautious about dealing with dietary needs. I always looked at it this way -- my child had to be ready to live in the real world by the time she left for college, which was two years ago. My job was to help her learn how to do that as safely as possible before she left the nest, which meant taking small baby-steps in independence throughout her childhood. That ranged from crossing the street by herself to crossing an ocean. For anyone who has the means an opportunity, I think resident camps offer valuable opportunities to learn and practice independence skills.