One of my children continued to receive invitations to the university’s summer program for HS students even two years after he had enrolled at that school. I think that was a matter of one department not communicating with another.
Re: Likely Letters. The other child received a LL from Columbia on March 1st, but I believe that is because Columbia invited him to participate in a Science Research Fellows Program. I had not realized that the program existed or that LL would be extended to anyone other than as described in this thread: URMs, women in Engineering, recruited athletes, etc.