These are all great points, and this is a personal decision how you want to handle it. You can take a bit of advice from everyone and use it to your best advantage.
However, from a pitcher's mom's point of view, I would first be more concerned with how much throwing your son will do in a week. That definetly needs to be discussed with the coach, do not hide the fact that your son has pitching lessons, this may do more harm than good in the long run. Your son making JV or Varsity may make a difference.