Our DD was contacted a week after her first 2 items were entered (showed her going in the system on the 22) then she posted her 3rd and 4th item. So I'm thinking there is NO rhyme or reason.
For which Academy? Each probably has their own criteria for when they schedule DoDMERB.
WP wants certain parts of your app to be complete before they schedule DoDMERB for the candidate.
Last year, USNA ordered it way before West Point did. It seemed as though WP required the personal statement to be completed, before they would order it, even if the rest of the file was complete.
It depends if you are applying to the academies of ROTC. The academies receive it during the application process, ROTC does not receive it until after a scholarship is rewarded or contracting on campus. Assuming you mean an academy though!!