at our school it does. The school asks that each family donate 10/wk to the church. The church supplements the school. The families tehn recieve a tax deduction to $520 for charity donations. Since non catholic families arent giving to the church that pays for alot of the school thier tuition is higher but only $1000 or less/yr higher.
Usually there is an increase in tuition for non-Church members. We're atheist but our kids go to a Catholic school because of circumstances. Tuition is a few hundred dollars more a year for us because we don't go to their church. To prove you are a member you are supposed to get little donation envelops from the school that are tagged with a # that represents your family and they check the offering after Mass to make sure everyone is going a majority of the time.
Our Catholic school has 30% of students being Non Catholic. It is a great education and faith based. Kids will learn some prayers and traditions that are Catholic, but I really like our school and wouldnt trade it for anything!