As mentioned already, a LOA is not a guarantee of an appointment. But yes, the LOA is given in reference to your recruitment as an athlete. But as mentioned, you aren't committed to being an athlete.
Now, whether that LOA would be taken away if you told the coach you weren't interested in playing; should you receive an appointment; no one can answer that question. It is quite possible that the LOA would be taken away. Thus, you'd be in the same position as every other applicant.
Having said that, I can tell you about a NUMBER of athletes who's #1 desire was to attend the academy, graduate, get commissioned, and become military officers. And I know quite a few "Recruited Athletes" (For lack of better terms) who used their athletics to receive their appointments. Then, once at the academy, they CHOSE to not be involved in the sport. They still get to be a cadet and remain at the academy. This isn't a college athletic scholarship. The military doesn't have those. So, if you USED your athletics to get an LOA and an appointment, and then once there give up on the athletics, you'll still be there as a cadet and get your degree, commission, and be an officer.
Of course, some will think this sucks. That if you weren't an athlete, and weren't recruited, you may or may not have received the appointment. But these same people think that most athletes aren't the same academic caliber as those applying to the academies who aren't recruited athletes. Me personally; I believe if you truly WANT to be a cadet, WANT to receive a degree from the academies, and WANT to serve your country as a commissioned officers, then do or use whatever it takes to get there. If that means using your athletic ability to get an appointment, then DO IT!!! Some people use their 4.0 gpa and AP/IB academics to do it. Some use their 35 ACT scores. Some use their JrROTC/CAP as their "Special Quality" to get an appointment. Some use their "Diversity" to receive an appointment. Everyone has strengths and weaknesses. It's up to use to exemplify your STRENGTHS in the application process to give you the edge in receiving an appointment. If one of your STRENGTHS is your athletic abilities, then USE IT to get you to the academy.
The academies are a Top-10 type of academic university. Whether you are there via sports, academics, extra curricular, etc. you are expected to be able to succeed academically and militarily and eventually become a commissioned officer and leader. If you think you have what it takes to succeed at the academy, then use WHATEVER STRENGTHS YOU HAVE to give yourself the edge and receive the appointment. If athletics helped you get there, and once there you choose not to participate in that IC sport, no big deal. I would recommend however that you wait until you receive the appointment and actually get through basic training before you decide or even mention not wanting to participate in sports.
best of luck.
