From what I know, I'm pretty sure neuropsychological testing is suggested for most testing accommodations and school accommodations as diagnoses such as ADHD/ADD cannot be confirmed without that, they're not really 'tick the boxes that apply' disorders, and require further neuropsychological testing. The reason it is normally required is that it is used to back up your claim that you need accommodations, as it has been explained to me. It's one thing to have a short letter saying you have ADD and require accommodations, it's a whole different thing to have a full extensive package of paperwork detailing exactly why you need these accommodations based on neuro testing (ie: student scored only 66% percentile on perceptual reasoning, 56% on working memory and 42% processing speed which means they require X amount of extra time). While it may not be needed, it is a surefire way to guarantee testing accommodations.
Not to be the cynic, but I imagine it is not that hard to get a simple note from a psychiatrist saying you have ADHD, whereas actually having the data to back it up almost guarantees your accommodations and further accommodations in university. From what I know in order to get accommodations: people have submitted their full neuropsychological workup because there needs to be proof that you require the accommodations you are asking for. Just my two cents. Also, submit now. If it is incomplete and they require more, they may tell you and you will have a chance to be able to redo your application for accommodations before the deadline (or so I believe). Might as well try!