Acupuncture is useful for all psychological conditions and they all are treated regularly and respond well clinically. Along those lines acupuncture does initiate/foster chemical changes in the body which often lead to permanent changes in these conditions. That said, Chinese Medicine does not treat "anxiety" per se or any other condition and techniques and needle depth have nothing to do with any of it - that is purely up to the practitioners training (i.e. one is not "better" than the other). Chinese Medicine does treat various patterns that lead to the symptom of anxiety, but trying to isolate the conditions to particular chemicals is the domain of western medicine - not Chinese Medicine. The page acupuncture treatment for anxiety has some of these patterns to give you an idea of how we view and treat anxiety. Also the article "What Does Acupuncture Treat?" has more information regarding diagnoses and the process used within Chinese Medicine.
With regards to APD, this is treatable as well, but again, what is treated from a Chinese perspective is their overall diagnosis, or pattern, and not chasing down individual conditions/symptoms. There are a range of psychological, auditory, and vision related issues all treated with acupuncture, but diagnosing and treating the underlying cause is the crucial aspect to proper treatment. So in many ways the western "diagnosis" is irrelevant.
All that said, the best answer is to take your son to a fully trained acupuncturist locally and let them properly diagnose and treat him. He should do well.