Let alone at a significant rate.
Why is this wild conjecture worth a discussion?
Give me a break.
As a clinician that evaluates disabilities, it is very difficult to fake one. They tend to be diagnosed at an early age, and not at "test time" in high school. In fact, as a person ages they are much less likely to receive a diagnosis. There has to be early-age evidence even if the diagnoses is later in life.
The disability rate in elite / prep schools exists but is low. These kids tend to be more on the spectrum than anything else.
Underperforming kids who don't have a disability, and might be prone to cheat by one means or another, and who aren't sports recruits tend to transfer to easier schools.
If a kid wants to go through the process of being fraudulently diagnosed by an independent psychologist with ADHD, for the purpose of accommodations, then the same process is discoverable by literally anyone with an internet connection. That is, by everyone.
And from what I know, this has much less to do with clinician corruption than it does with the individual faking symptoms. There's few to zero people risking their licenses to hand out fake diagnoses for scheduled medications that are under heavy scrutiny at all times by the States and the Feds. The liability alone is off of the charts.
Schools are only likely to accept the diagnoses if a thorough clinical evaluation is undertaken. The result of which is not able to be faked.