Yes, for people who have an allergy or an intolerance to a particular food, their body will crave it.
When I was a teenager, I literally could and did drink entire gallons of milk all by myself. I loved and ate lots and lots of ice cream.
As an adult, I loved eating crusty artisan breads. Didn't matter what kind; I ate anything. Sometimes, that was all I ate for a meal--crusty bread with lots of butter.
Come to find out that I have a casein allergy (bye, bye all cow dairy) and that I have gluten intolerance (bye, bye, all that absolutely wonderful, yeasty wheaty bread!).
If he is getting a rash after eating strawberries--he needs to stop eating them. If he doesn't, he will end up with Leaky Gut, which will then allow more and different foods to enter his body through his damaged gut, thus setting him up for more food allergies and intolerances.
You can try to introduce them to him when he's older and see how he does. But for now, he has to stay away from them.