Of course each school's admission criteria and HC's clout with the admission office varies. My son did encounter a situation with a HA engineering school in the Midwest where the school got in trouble with the NCAA for having "too much" coach influence in admissions. In that case, that coach was really looking for kids who were so strong academically that he would not have to worry about them getting through admissions. So for that HA, a kid with really strong credentials is going to be a huge preference for the coach. Of course, then the conversations turns to the coach pushing for the Early Decision application, which was my son was never going to do (too many uncertainties in his search and he did not want to be bound by ED).
I would never worry about a kid being so strong academically to not need the coach's support. A coach should at least run the academic credentials (transcript, test results) through admissions for a "pre-read" and that way the student knows the coach is sincerely interested and both the student and coach can get a non-binding but pretty solid read on his admission chances. A positive read and then the coach can talk specifics about how firm the roster spot is.