Does your son have an admission's counselor that he has also been communicating with? If so, I think it is reasonable for him to ask if his file is flagged as a recruit. My son was in the same boat applying at a different SA. He had been talking to the coach, but we couldn't gauge who had the most interest, our son or the coach or mutual. In a phone call with his Admission's counselor clarifying something else in his file, he just mentioned he had been talking to Coach X and the counselor was like, oh yeah, I see your file is noted as a recruit. It helped clarify it without our son having to come right out and ask the coach. However, at the end of the day, these kids are getting in on a lot more than athletics. It seems coaches at the academies only have so much "pull" My DS's number one choice is a nomination required SA and the Coach ends every contact with, get your nomination! So, it seems somethings can't be worked around easily, even for recruits.
However, given everything you said, it's probably a safe bet to assume he's a legit recruit. GOOD LUCK!