I was diagnosed with ADHD with my severity level being somewhere around the 97th or 98th percentile while in college--studying psychology, ironically enough. I was part of a research study where cat scans and brain imaging was used to "map" the brains of the participants after different interventions. The researcher at my school and I began discussing the different results and I was surprised when she told me coffee would help people with ADHD. Often ADHD's underlying cause is a lack of functioning neurotransmitters in the synaptic cleft of the neuron responsible for passing along information. Basically--there aren't enough little message carriers making it to their destination--the next neuron. So, the message that came from the original brain neuron intended for another brain neuron will often stop before it reaches the final destination. It's sort of like the neuron short circuiting and stopping temporarily--the signal gets lost. (I wish I could draw a diagram on here--it's how I finally understood it! ) Ritalin, Concerta, and many other ADHD "medicines" are really just stimulants. They work the same way coffee does. Basically, they stimulate the neurons to release more neurotransmitters than they are used to--which helps the message get to where it needs to.
However, some research in its infancy is starting to show that these stimulant drugs (and coffee falls into this category) can do more harm than good in the long run. Yes, the child may be sitting still right now, but with repeated stimulation of the nervous system comes issues. That means that the neurons are being overworked and overstressed constantly. In addition, your body has to process out much more stimulant than it is used to. Think about it--if you overstimulate your pituitary glad for too long, what happens? It breaks down. While much more research needs to be done on these effects, using caffeine and other stimulants to treat ADHD may not be the best idea.