Oddly enough, you may find the exact opposite trend in a case like this. City College of New York was founded in the 1840s by a wealthy business leader who also served as the president of the city's Board of Education. It remained a "free" college until it began charging tuition in the 1970s, and as a result of this it was extremely difficult to get into the school. It was head and shoulders above other public colleges in the U.S. over that period, and I believe it still holds a distinction with more Nobel laureates among its graduates than any other public college in the U.S.
Personally, I think any "free" New York colleges are going to get filled with Asian students who are the children of recent immigrants.