As of a few years ago (and I believe still is accurate today), USNA's position on learning disabilities (my term) such as ADHD, ADD, dyslexia, etc. is the following:
If a candidate has demonstrated that he/she can function/perform at an acceptable level WITHOUT special accommodations (i.e., extra time, sitting in front of the class, medication, etc.), learning disabilities generally won't be an issue. If, however, the candidate needs special accommodations, the candidate won't be admitted.
The reason, as stated by USNA, is that the military cannot guarantee that there will be "extra time" for certain evolutions or that the person can alway sit up front, or that medication will be available, etc.
I don't recall how long (i.e., the time period) a candidate has to be without special accommodations in order to demonstrate he/she can handle the situation. I don't believe it is all of high school -- I have some vague recollection it's a year, but could well be wrong about that. You should check with DODMERB.
One other point -- I can't say that learning disabilities (with or w/o accommodation) would be an issue for NASS; not sure what is asked about those or other medical issues in the application. I do agree that standardized tests that are untimed would not count for USNA/NASS purposes.