If a candidate reports for I-Day, gets released because of medical, the good chance is he will be DQ's from NROTC at the same time, thus preventing the NROTC scholarship from "kicking in". NROTC waiver authority is different from USNA so absolutely a waiver is possible, the big question I would have is can NROTC initiate and grant a waiver fast enough for the candidate to attend NSI and have the scholarship activated in time? I would guess it would be very difficult, unless they could schedule the candidate for the last NSI and get any waiver approved prior to that. But there is always "College Programmer" for NROTC, where a candidate can actually (at least last year) walk on at the start of the fall semester, and join without the scholarship for the first year. That would give NROTC waiver authority time to process and approve the waiver, then a "side load" three year scholarship thru his Battalion would be available and likely.
On another front....there are circumstances where you have to make a decision early for a civilian college. Most "Full-Ride" academic scholarships, and athletic scholarships require a true commitment at the time of offer, meaning any SA applications ethically need to be withdrawn or closed since there has been formal acceptance to attend the school with the scholarship. This is from personal knowledge, and is usually spelled out in the offer. I have no idea of any consequences if you don't follow the ethical route (there is another thread on here regarding multiple acceptances and in that thread someone related that USNA was notified thru the generic college something or other of the applicants decision, and his USNA app was terminated). I have no direct knowledge of this, but I could see a college that reserves a full scholarship and then an applicant goes someplace else at the last minute having hard feelings, and possibly legal repercussions (repayment of the full scholarship) if you legally agree (many full scholarships require signing documents of commitment). As long as the actual "commitment date" is late enough you can keep all options going, but once anything is signed or acknowledged be careful, JMHO..