My kids went to several different catholic high schools. And yes there was a relationship and an advantage. One went to what is considered a feeder school. Lots of high performing kids with high stats were accepted to highly ranked catholic colleges. But these same kids were also accepted to other top 20 schools. these kids all had the stats and ec to get in. What was and is more common here, is that the local catholic colleges, some of which have a national reputation, would have an instant admission day at the high schools. They would set the minimums they require, say 1250 sat and 3.5 gpa and the kids would sign up and meet with the college rep at the high school and get instant admission and a financial aid scholarship estimate. The kids find out that day after a 10 minute conversation whether they are admitted or not. Most of the students take advantage of this even if they decide not to attend. The colleges know the caliber of the students they are getting and the students know they have a college to go to. Everybody benefits.