My son, who received an appointment to West Point (although several years ago now), played club lacrosse not associated with his high school. He listed it as his varsity sport and it seemed to be fine. He went to a small high school that did not have a lot of sports options. I think he talked about it with his HS adviser about it to make sure he understood the situation.
Not sure if it matters but my son decided against attending WP and went AROTC instead. He is now a happy 1LT, forward support company XO.