You're talking about my school, the New Mexico Military Institute.
If your DS/DD attends as a sponsored prep, does well academically and does well in the corps of cadets, yes it is guaranteed. I know that the academy requires a 2.2 GPA while at NMMI to ensure their appointment.
Conversely, if your DS/DD is in my situation and is a self-prep for a service academy(USNA for me), then no, it does not guarantee an appointment, it does, however, help. NMMI is the second best junior college in the country and is a foundation school for every academy except for USCGA. The academy knows the difficulties of the academics, athletics, and rigors of the corps. Either way, I highly recommend NMMI for a prep school for any service academy.