An offer of appointment requires fully qualified candidates (that means full disposition of the 3Qs: Admissions Board, physical/CFA, and medical/DODMERB) who are listed on a nominating slate. Admissions, theoretically, can review slates as soon as the Admissions Board reviews all candidates...but other factors could come into play (which is why Admissions might wait for all Qs to be determined). For example, if Admissions has identified a potential slate winner but their CFA or DODMERB is not complete...well that slate might not be decided until there is disposition for the CFA/DODMERB. If the same candidate were to be medically DQ'd, but the medical condition is waiverable, then the waiver process must occur first. If the waiver is granted (presuming they also pass CFA), then that candidate might receive the appointment and if the waiver is not granted, someone else might be looked at to win the slate. Also, if USNA decides that this candidate should be charged to a different nomination (VP/ROTC/JROTC/POTUS/SUPT/etc), then the slate might have to get reviewed again. Bottom line, there is no rhyme or reason or anyway that one could really know when a slate is reviewed. Many (if not most) candidates will arrive on I-Day and graduate from USNA never knowing who actually nominated them. I realize that many individuals will be curious about this process in the next few months...but it isn't even worth a few seconds of your time to try and figure out if a particular slate has been reviewed.
From my understanding, MOCs can see a candidate's status -- similar to what BGOs see. I believe they also submit their slates online now...which is why someone mentioned that the nomination had shown on their portal two days after their interview.