I've mentioned quite a a few times; even recently in a thread in the nominations sections, that there are times when a MOC can't get a full slate of 10 nominees. I've never seen a MOC with only 1 nominee; but I have seen slates that had less than the max 10. Most people are in a position where there's a lot more applicants for nominations than there are slots available. So it's very competitive. But there are some congressional districts in the country; in rather large states; where military service is not very popular, and not as many people apply to the academies.
To answer your question: All based on "IF"
1. IF the MOC has a vacant slot at the academy; (They are allowed 5 cadets at the academy at one time that S/He has nominated). Appointees from the national pool don't count towards their 5. So IF the MOC has a vacant slot, then the academy MUST APPOINT a nomination from their list if one is qualified 100%.
2. IF the MOC's vacant list only has 1 nominee (This would be so rare) and that nominee is 100% qualified, then YES, the academy would have to choose that one person.
3. If that one person was not 100% qualified at the time of INITIAL selection; e.g. they were waiting on a medical waiver; it's possible that once the waiver was/if approved, the individual would be in the national pool for consideration and the MOC would get 2 open slots for the following year.
You said that your MOC posted their list of nominees and there was only one person on it. I'd probably try and verify and clarify the list. It's possible that the MOC chooses a PRINCIPAL Nominee; which is a 100% guaranteed appointment, and they only listed that one name; and the other 9 are going to the national pool. It's also possible that s/he listed the individual who received an appointment, and it appeared to be their entire list. Simply saying you might want to clarify what they posted.
But again; IF the MOC has an available slot for that class; and IF the MOC only had 1 person apply for a nomination and they received that nomination; and IF that individual is 100% qualified for the academy during the initial selection of appointments by the academy; (Initial appointments for MOC slates are done before the national pool is done); then YES, that one individual would pretty much be guaranteed the appointment.