I'm not sure about "most", and I can only speak from my limited experience, but here is one observation. My DS is a recruited athlete (not Football or Lacrosse), as was a high school teammate of his from last year who is now a plebe. Their experiences have been somewhat similar.
In the case of his teammate from last year who is now a plebe, he received an LOA around September, his nomination in (I think) January, and I am not sure when he received his appointment.
In my son's case, fingers are still crossed. He attended summer seminar in June and was also invited on an official visit in September. He verbally committed to Navy two weeks ago, and the coach said that the next step would be to see whether he would receive an LOA. So, yes, he is certainly hoping for one. Nothing of course is guaranteed.