Even though ADHD is insanely over-diagnosed in this country, I would imagine there would be a very strong similarity in rates of drug use between those diagnosed with ADHD accurately by a full-battery with a competent child psychologist and those diagnosed on a psychiatrist's whim. Very few well-behaved A students are diagnosed, and whether the child is legitimately ADHD or acting up and unable to focus due to personal reasons, the diagnosis is almost always given as a child is struggling (or else why visit a psych doctor?). Kids who struggle during their formative years are more likely to use drugs, and I have to imagine giving very young children powerful dopaminergic stimulants to take 5+ days a week for a couple years also has some effect on the development of their neurological system.
You throw in a diagnosis that remains a part of a child's psyche and concept of self-identity (believing yourself to be disabled isn't healthy, not with something as subtle as ADHD) and you have a recipe for all sorts of bad behavior once they come of age. Now that ADHD isn't as serious a diagnosis (parents don't flip out about it and kids understand it to be relatively normal), it seems that Autism Spectrum disorders like Aspergers are all the rage. I know quite a few kids who are diagnosed, and to me they just seem like kids who are more socially withdrawn growing up in a generation where video games rule their entire day. They aren't as socially developed as they should be because they are playing video games alone and communicating online with people who act crazy while anonymous, and they are "obsessed" with video games because they cause some intense fucking neurotransmitter release, but I imagine when they arrive in high school and social interaction becomes much more of a desire and necessity they will catch up and develop the lacking social skills.
So yes, there is a correlation between being told your brain is all fucked up when you are six years old because you do not fit in with the rigid structure of elementary education, and I imagine that those who actually have ADHD (I definitely really have it, and I am upset at the over-diagnosis of these disorders because they devalue the validity of a true diagnosis, amongst other major issues) probably use drugs at rates consistent with those of people who have been falsely convinced by incompetent doctors that they have a disorder. Child psych doctors find it easier to blame the neurophysiology of the kid than to risk losing the parents who pay for their children's visits by pointing out that their home environment is unhealthy, and that the burden of their kids problems are on their backs for all the domestic disruptions (exposure to divorce, affairs, witnessing/suffering verbal abuse, physical abuse, etc etc..). All that shit will make concentrating difficult for a child and lead to a certain degree of acting out, perceived as hyperactivity in children, which can lead to an ADHD diagnosis. As the children grow, drugs are only a natural progression as a form of acting out, and they feel really really good and allow some young teens their first taste of inner-peace in several years.