I mean this in the kindest possible way, but ...
Maybe if you mean "catholic" with a lowercase c, but not in the case of Roman Catholic. My metro area has
twenty-seven Roman Catholic high schools, and only five of them are co-ed. There is a *definite* socio-economic hierarchy in those schools, and their administrations' attempts to add economic diversity via student aid only go so far. (Generally speaking, the co-ed schools are going to have the most economic diversity, as they are the cheapest -- but they also have the reputation of being willing to take anybody, so most kids are going to prefer the schools that have higher academic performance standards for admission, because they don't want to be perceived as too stupid to have gotten into them.)
The most prestigious debut event here is related to the Church; the girls are presented to the Archbishop. There are some schools where attending is nearly de rigueur, and others where almost no one knows that that ball exists. At the schools where it is expected, the right shoes and the right cars really count, as do the right clothes at outside social events (and being invited to the "right" outside social events -- escorted by boys from the "right" schools, of course.)
In small towns you see more economic mixing because there are fewer school choices, but in bigger cities where there are a wide range of choices, there are plenty of opportunities to discriminate based on wealth. The kids who get in to prestigious Catholic prep schools on scholarships do make useful connections, but they are always remembered as being the scholarship kids -- everyone knows exactly who they are and what their economic circumstances are..
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