The only thing keeping a NESCAC from accepting a whole team as recruits is the agreement through the conference. Since D3 doesn’t give scholarships every single player could be admitted to the school as a recruit, but the schools in the conference have agreed not to do that. The admissions office may also want the athlete for one of its other hooks (URM, male/female ratio, legacy) or just good stats so will let the coaches know. There are also 2 sport athletes so it might be better for the field hockey coach to support the girl leaving an extra slot for the lax coach. There is also trading of slots from one team to another, but keeping the school under the total number agree to in the conference.
I don’t think there are a lot of surprises where the coach thinks the applicant doesn’t need support but then the admissions office decides not to admit. There is a lot of communication between the coaches and admissions.