Unlikely to outgrow. People usually do not outgrow peanut allergy, so one can get his blood tested or his skin tested, and then see the allergist to perhaps eat a peanut butter cookie at the allergist's office, and stay there for a while to watch for any reactions. Anaphylaxis can occur with peanut allergy, so patients usually carry an epi-pen self-injector for emergencies.
Children maybe. Current data suggest that about 20% of children may "outgrow" peanut allergy. Most of these are younger children with milder reactions. A person who has had a severe, anaphylactic reaction, who has a very large skin test or very high ige blood test to peanut is unlikely to outgrow their peanut allergy. Adults are less likely to outgrow peanut allergy.