J.W.
GABA is a calming neurotransmitter. It is an ingredient in a supplement called Nutrasleep that helps some in my family sleep better. As to whether or not it will help your son's ADHD symptoms is something nobody can answer because what is causing the symptoms can be so varied.
My own daughter had been diagnosed with ADHD because of inattention and lack of concentration, but she had not been thoroughly vision tested, endocrine tested, had a sleep study done... nothing! What the psychiatrist at least had done was ruled out parenting issues and environmental factors - such as TV watching and video games. I do believe allergies did contribute to it! He also had her do testing to rule-IN ADHD and it said she DID have ADHD but in the end... she did not. She was given medications with bad results because she did not have TRUE "ADHD" - where the frontal cortex maybe isn't developed as well or something. Here is something to read about what else the same symptoms can be: http://itsnotmental.blogspot.com/2009/04/is-it-adhd-atten...
At least the supplements are so very benign, and I am amazed how the psychiatrist was not "afraid" of amphetamines and antipsychotics, antidepressants, benzodiazapines, etc used with children but was "afraid" of food stuff. People died from what he gave my kids but no one ever died from those supplements.
Anyway, back to your GABA question.... Here are questions to ask yourself - How is your son's sleep? Is he anxious? If so, GABA maybe can help. Fish oil is also very important for growing brain cells, as is attention-extending activities slowly increasing attention span.
There has also been some positive results in research studies showing the EMPowerplus supplement may help with ADHD in adults, so you may want to look into that as well - www.TrueHope.com (call them - they do have a powder form for children, but you should ask about it, and of course consult your child's pediatrician.)