One of my daughter's schools last year told her the same thing after the 2nd board preparing her for if she did not get one the third board, she did so it was a mute point. But basically they had a spring board for incoming freshman and in that school's case only looked at those who had completed a national application. For those that had not, that process happened first part of the school year, this is the same school that @AROTC-dad
's son went in, as he says a "walk on", did well and ended up with a 3.5 year scholarship. Definitely having those conversations with the ROO at all potential schools is a good idea. Each school and each brigade handles all of the "extra money" very differently.
So yes there should not be another application, they just need to go you plan on going there.