There is no reliable test for ADHD. Was he diagnosed via a questionnaire? What kind of professional diagnosed him?
COVID caused a lot of distraction for many students. Have you considered he might also have some sort of screen/social media/phone addiction going on?
So with ADHD in our public school, students have 504 plans, If you add in other learning challenges, it could be an IEP. Private schools generally don’t accommodate as well, at least in the experience of people we know, some of whom switched to public schools. However, if he does decently he could be refused services. I wonder what testing he has had and what the results were?
I really feel that people overestimate what Offices of Disabilities can do. THey generally give the student letters to give the professors, which may or may not list accommodations and will not disclose the disability. It is up to the student to give these letters to the professor and, basically, negotiate. When problems arise it is often a dean, doctor or other professional involved who will advocate for the student with a professor, and some professors are more accommodating than others.
Back to you original question. ADHD is not relevant to admissions. Schools will not discriminate and many brilliant and accomplished people have ADHD. But there is no obligation to disclose before admission, and it should not be used to explain grades which, as others have said, sounds like making excuses.
If he is inspired to write an essay about it, fine. If it is done right it can be an interesting and likable essay. But in some ways I would hope he has better things to write about. He can also write about it briefly in the supplementary essay. My kid that about their type 1 diabetes. He does not need to disclose at all.
Are you sure a gap year it the best course? Have you looked at Landmark’s summer program or bridge program or whatever they can offer? They also will refer you to coaches.
I would encourage applying to whatever schools he likes that match his abilities. Reach, match and safety like everyone else.
Full disclosure I have a kid with ADHD but also bipolar 1, who went to college, left, worked, took community college classes, entered a degree completion progrram for adults and graduates at age 30 this December. Yay! It isn’t a tragedy. Not saying that will happen, but I think we parents can stop being so afraid. We can just help them follow their own choices. He will have to advocate for himself at school, but many schools do offer extensive supports, including weekly meetings for time management- and you can always hire a coach if you can afford it.
Oh-and yes, consider tuition refund insurance but check to see if your son’s diagnoses are covered.