I agree with @twoinanddone. In a recent conversation with a NESCAC coach the coach commented about the high number of first gen kids on their team and about a high school where they’d found some really great URM kids.
They mentioned that getting such kids also allowed them to admit a few “white kids from Connecticut.”
IOW, it was clear admissions was more likely to accept players they wanted, with or without formal support, if they were making a real effort to meet the school’s other admissions goals.
I think part of the answer to the OP’s question depends on how closely the coaches are working with admissions. At this coach’s school admissions has made a concerted effort to work with coaches so that there are no surprises in the admissions process. I think this is common among the NESCACs. I’d ask the coach directly if he’s ever been surprised by an admissions decision.