My son is a freshman at a Jesuit high school and absolutely loves the experience so far. We are not a Catholic family but he had no problem fitting in and being accepted. He was concerned not knowing many other kids at the school but almost everyone was in the same boat. Playing sports or having other common interests helps create friendships. Many of the freshman baseball players quickly became good friends.
His school is very strict and the students must show proper respect for their teachers and other students. He has an hour or two of homework each night. He does not have much time to socialize with his public school friends and former teammates which can lead to some hard feelings between old friends. On the positive side, his new friends are more focused on school and performing their best in sports and other extracurricular activities. Many of the baseball players are practicing or lifting a couple of hours every day after school. This has made him more focused and determined to work hard. There are a couple of upperclassmen who have commitments to D1 schools who help lead and motivate the underclassmen.
If the school you are considering is like my son's school, I would first determine if he wants to be in that type of environment. If he is disciplined and goal oriented he will do great. I don't think the coach would make the suggestion unless he thought your son would succeed. In the end, your family will need to make the decision based on how well the school will fit into your son's goals after high school.