If your son scored a 1350 on his first try, I would think he can get solidly over 1400 with some more practice, studying and super scoring. If so, then I think he can be worked in, if his baseball skills are there.
What sticks out for me is your "if he gets noticed" comment. Columbia was actually the first school to reach out to my son. That was the summer of his rising junior year. Dartmouth was also interested. May sound crazy, but we didn't take them too seriously and didn't follow up on campus invites, as we were concerned with son's ability to keep up at an Ivy school...he did not have your son's grades. Unweighted 3.9 passes the bar and 1350 first pass isn't bad. May also want to go the ACT route.
Point is, if Columbia is high on your son's list, but you haven't heard from the school, reach out to them yourself. But, also important are his baseball measurables. If he's mid-80s and also projectable, you've got something to work with and you should let them know.