Yes, the Aspen Institute has research showing this great benefit of kids being physically active.
There is separate research which show active kids do better in the classroom. This is primarily due to the increased blood flow to the brain. Check out the academic benefits of physical activity HERE.
The impact of physical activity and sport is most visible with women. 96% of all 'C Level' female executives grew up playing sports. We need to make sure ALL kids get active to give them a chance to be successful in their careers...and in life.