Absolutely! Diet and behavior are related and there’s no way to deny it.
The medical condition you are referring to is most often called Attention Deficit Hyperactivity Disorder. It probably has to do with a minor chemical imbalance in the brains which leads to hyperactive behavior. This means the child doesn’t sit still well, doesn’t learn well, doesn’t focus well, and doesn’t make friends well.
While it’s still being debated, research published in respected pediatric journals has established that sugar increases hyperactive behavior causing children to be jumpy and cranky. The additives in processed foods are also culprits when children have behavior disorders. My best advice is to keep your youngster on a diet of lots of fruits, vegetables, and grains. They’ll feel lighter and feel more like running and playing. They’re just going to be happier, healthier children all around.