Medical qualification is not subject to the Jan. 31 deadline. You must be medically qualified before you can receive an appointment, which is obviously before I-Day. It need not necessarily be by April 15, if the issue is likely to resolve prior to I-Day. USNA might give you an LOA conditioned on medical clearing or take some other step to let you know you have an appointment subject to medical. Most medical issues, however, are resolved by mid-April.
Also, if DODMERB DQs, a waiver request happens automatically. However, USNA doesn't review those requests until they decide they are likely (or certain) to offer someone an appointment. So some candidates may never have their waiver requests evaluated.