You might be able to go directly to seminary after USNA (if you are lucky… and good) but you cannot do them simultaneously.
Also, contact the Archdiocese for the Military Services. They probably can provide some guidance.
http://www.milarch.org/site/c.dwJXKgOUJiIaG/b.6287817/k.290A/Archdiocese_for_the_Military_USA.htm
I get their newsletter, and last year they profiled an Air Force Academy graduate who attended seminary and became a chaplain. If I recall correctly, he went directly to seminary from the academy.
P.S. I just noticed that @zapfino already provided the link to the Archdiocese for the Military Services.
Oh well, two can’t hurt.