I have never seen published minimum SAT requirements for USNA. There are eligibility requirements like US citizen, unmarried, no dependents, etc. Advancing from preliminary application to official candidate means you meet some sort of minimum to be considered. USNA states:
"If you are found scholastically qualified but do not receive a Letter of Assurance, you will be competing for an Offer of Appointment from within your nominating sources. Approximately 2,000 candidates are found fully qualified (scholastic, medical, CFA, and have obtained a nomination) each year. Of that number, about 1,500 will receive appointments and approximately 1,200 become midshipmen."
Again, I have never seen a published definition of "scholastically qualified" for USNA. (please correct me if I am wrong, I would like to see that source).
Academic "minimums" for NAPS would be even lower, if they even exist. The purpose of NAPS is to allow the candidate to mature and improve, prior to starting at USNA.
You can view the published class portrait, which shows the middle 50th percentile. But that means that there were students admitted with scores higher and scores lower. How low, who knows.
So, there is always a chance, however better academic achievement gives a better chance. I would much prefer being above average than below average.