YES, because federal and state laws began outlawing segregation in public schools beginning in the 1940s.
A good example is NJ, which rewrote its Constitution in 1947. The convention was held in the Rutgers gymnasium on College Ave, still in use today. The issue might have been overlooked if not for a black member of the convention. As a result, schools began to desegregate. There were even all-black schools which either dissolved or desegregated as a result.
In the 1950s there was the famous Brown vs. Board of Education case, which put an end to segregation in pubic schools. There followed the famous 1957 Little Rock Arkansas forced desegregation, dramatized in Forrest Gump.
By the 1960s, all public schools were desegregated.
As a footnote, American universities began accepting female students in the 1960s. Rutgers, a state university, admitted women for the first time in 1963, and Princeton, a private university, in 1969.
BUT, there is also a footnote concerning blacks at universities: you should know the story of James Meredith: