There has been some study that shows the school itself correlated with post school achievement with a large caveat: those who were accepted to “higher” quality schools but ended up attending a lower regarded institution did just as well. The implication being it has less to do with the school and more to do with the students who can get accepted to those schools.[1] There was a comparatively larger impact on those coming from lower level income families.

There’s also been some follow on studies that look for differences in the effect depending on race and gender

[1]https://scholar.google.com/scholar?hl=en&as_sdt=0%2C32&q=Kru...