I have a child with ADHD and think that unless someone is desperately poor, using SSI (disability) for something like this borders on fraud. I know that technically it's doable and that if I have a problem with this that I should work to change the law, but I think it's wrong to access those funds for something like this unless it legitimately interferes with your ability to work.
To me, disability payments are for children who are permanently physically disabled, need round the clock care, are terminally ill, or so mentally unstable that they cannot attend school or be left in an after school program. My friend whose son has quadriplegic cerebral palsy, a ventilator, & 2 GI tubes should be getting disability to help offset the financial burden of her son's care. My friend whose son has mitochondrial disease and is on portable oxygen and a feeding tube needs this. The families I know where children have Down's Syndrome or are blind and go to special schools need this. ADHD? I don't think so.
Your son is fine. Don't label him as "disabled" so that you can collect extra $$.
ETA: Interesting that you TOTALLY CHANGED the question. For anyone interested, the original question was about whether or not she could and should apply for this for her son because she knows of other families where the children get disability for ADHD. THAT is why the initial responses were so strongly against using that.