One sport is better than none.
However, there are a couple of problems with your plan. First, without ever having played sports in high school, do you think that there is one that you can step into as a super-senior and do well enough to get a varsity letter? Secondly, there would be the question of whether you have eligibility for a high school sport as a super-senior. Depending on your location, most state high school athletic associations only allow 4 years of athletic eligibility to any student. Just by attending a high school for a year you use up a year of eligibility whether you played a sport or not. That is something that you would have to discuss with your coach or your school's athletic director.
Good luck with your application to USMA!
Stealth_81