There's something to this theory. In the middle 1980's, and Denver psychologist and columnist, Joan Beck IIRC, wrote a series of articles on martial arts and kids with ADD (now called ADHD).
A very high percentage of formerly medicated kids were able to get off the drugs after only a few months of participation in martial arts classes. It didn't seem to matter which particular style. What mattered was that there was a good combination of class structure, physical plus mental exercises, and and a progression of goals + achievements + rewards.
They had to do a study? I thought the results would be obvious...