I can only offer our experience with admissions and with a friends's son who graduated last year. It does offer support and modification of work, but the student still has to fit into what is a very structured program. Think of it more along the lines of accommodation, so if your child needs special instruction, this will not happen. They are looking for kids who can master and adapt to the school environment and eventually not need the program. In other words, two years of support and then you are on your own essentially. If you need support all 4 years, you'll get it.
This was very tough on friend's son who really struggled with a science class in senior year and nearly failed it.
In our case, we had a very positive interview and DH was a graduate, so we were surprised when DC was waitlisted and then turned down. The program has a finite number of students - about 45, so they cap the program. Freshman acceptances are contingent on the number of applicants already in the program and how many they can add. Thus, the program is very competitive.
If you are interested in Catholic High Schools, there is a schools open house for special needs held each spring by the Archdiocese. DC nearly went to Archbishop Carroll, but we decided to go public. They have a small spec ed program, but they don't advertise it the way St. John's does.