Many schools do, esp with certain sports. There was an expansion of LAX teams at midwest colleges awhile back for this reason - they wanted to keep those full pay kids from going east.
It does.
One NESCAC (Amherst, who made their athletic impact study available) actually encourages coaches to bring athletes who are first gen/low income or URM to admissions attention so they won’t be counted against that coach’s quota - because that particular school actively looks for those kids. That is likely not the case at every NESCAC, they vary a lot in mission and resources.