Though this would not involve attending USNA, perhaps you could complete a major to prepare you for seminary studies at another college, while also participating in the NROTC program.
Also, check this link: http://www.milarch.org/site/c.dwJXKgOUJiIaG/b.7711371/k.F605/Paths_to_become_a_Catholic_Military_Chaplain.htm.