No. Based on the coaches I've seen for sports, selecting captains often come from the people who put in the most hard work, think of the team first, and exemplify leadership qualities. Not always the best athletes. The goal shouldn't be to be the star of the team, it should be to be an active part of the team and put forth the best effort. This is what coaches recognize and come time when you are looking for a recommendation letter, will often get a better response. If you can do all of that and be a stellar athlete, that certainly helps!
There are plenty of big fish "stars" in little ponds that get eaten up and spit out at the higher and more competitive areas.
As my son says, people go to a service academy to serve and lead in the armed forces, not to become the next sports star. Everyone at the school is on a full ride scholarship, not just the athletes.