Just about every sport has some sort of walk on or invitation policy. I.e. after BCT, the football coach holds an open walkon tryout if cadets are interested. Many of the sports that don't compete right away; (Football starts the actual season 3 weeks after BCT); have time. You can contact the team and ask their policy.
Now; how hard is it to get on/stay on the team compared to a recruited athlete? That is a difficult question to answer. It depends on the sport; if there's a lot of recruits, etc... For football, there are 50-60 recruited athletes between direct entries and the prep schools. Everyone of them was recruited because they've been playing football for a long time. Half of these recruits will probably not be on the team after the following spring practice in their freshman C4C year. Because the academy doesn't give out scholarships for athletics, they can recruit a lot of players and keep the ones who work out. Obviously those who don't stay on the team are still in the academy. (Unless they quit the academy, which some do because they really only came to play a sport). But MOST of those cut from the team will stay at the academy, find plenty of other things to do, and graduate and become great officers. Each team is different. Basketball has a lot less players than football or baseball. Each team is different. If it's a winter/spring/summer sport; talk to the coach of the team after basic and once you get settled in. If it's a fall sport like football, soccer, etc... they usually contact you in BCT to tell you about their open tryout policy.
As for fencing; fencersmom is on this forum a lot. She has boys in the academy who fence. *Hence, her screen name". She can answer directly many of the questions concerning fencing.