Bucs is spot on. It was our experience over the last few years with our 2018, that HYP have a higher academic bar (higher AI) for their baseball recruits. I would say 30+ ACT for HYP and 26+ for the others (Wharton at 30). Son was focused on Ivy schools and other high academic D1s (Northwestern, Duke, etc) and had a good experience with the schools communicating to him early in the process where the test score and grades/AP classes needed to be for an offer. Our son took the ACT early, posted a high score (in the 30s), so we were confident that test threshold was met as he received offers. The Ivys typically do a very good job of not making offers until the test scores have been met, and the path for keeping a strong GPA is clear. All the Ivy offers I am aware of have only been made after the "pre-read" is done by their admissions office, so getting that blessing should give some good comfort.
After our son received an Ivy offer during his junior year, it was made very clear by the HC that he needed to continue to perform academically - in his case that meant continued good grades in AP classes since his test score was good. Clearly the final admission to the school was a decision to be made by the admissions office, not the baseball program, so no letting up on academics. The AI score for the player is extremely important, so any material reduction in the score (or behavior issues) would put the offer at risk.
I recently heard of a local player losing his offer from a very high academic school (non-Ivy) after being committed for over a year due to failing to meet the admission requirements (a higher risk when committing to a school so early in high school). So in this case, yes, his offer was contingent on achieving a certain test score.
So much great information on this site that helped us through the process. Kudos to all of your sharing your wisdom and experiences.