Untreated / uncontrolled ADHD affects the ability to learn. My son had subject acceleration before ADHD dx/rx. We really didn't know what he is capable of until after getting his ADHD symptoms controlled. He made leaps in his academics with ADH treatment!
Also, in terms of academic outcomes, IQ is not a predictor of academic success. ADHD predicts negative academic outcomes elementary through college. However, there are specific organizational skills specific to the academic environment which predict academic outcomes.
Untreated ADHD symptoms interfere with learning.
At age 6, my son's FSIQ was 108 (a bit above average). At age 7 he was diagnosed with ADHD. Retested IQ at age 8 after treating his ADHD. FSIQ up to 132, GAI 141. (GAI is a calculation of IQ which adjusts for slow processing speed and low working memory - 2 hallmarks of ADHD which affect IQ testing.)
After 1 school year with ADHD treatment, my son skipped 3 grades, with additional subject acceleration up 2 more grade levels in three subjects.
There is valid reasoning why ADHD-symptoms need to be controlled before some accelerations. I understand that point of view. However, I see the other side. When my son was 6, he was in public 1st grade. He had behavior problems that were minor enough to slip by the school but significant enough that he was socially ostracized. He was acting out in boredom - and not surprising since the classroom pace was too slow for him and the material he had mastered years before.
I'd encourage you to look into Organizational Skills Training for ADHD (book). When your son has opportunity for subject acceleration or a gifted program, he'll likely need the skills. These skills might help the school view him as "ready" for the gifted program.
I'm looking at doing a 504 plan for my son this year to get a behavior contract with the school. Is a 504 an option with private schools?