I think the famous university counts more. However, there are respective old boys groups in an organization and there is advantage in career path. Moreover, boss tends to have preceptions, whether good or bad, on graduates on different school. It is exhaustive but holds a lot of true. I am father in late 30 and I have experienced and saw a lot of this unfair practices happened.
Only boss or businessman having their own enterprises would not fall into this game as they hire people working for them.
Firstly, I think the so-call 名校 must have something that make them famous, mostly because of their academic results. So I think we should not think 名校 is just a sign. They do have their way of nuturing the kids.
famous primary schools do not equate to good jobs as nobody would write the name of the primary schools in the CV, or seldom secondary schools. So as long as the kids could get into university, it's fine. Whether you get a good job after graduation is a combination of academic results at universities, interpersonal skills, appearance (which is proven to be very important in fact) and luck. Thereafter, it more relies on the individual's job performance and credibility at work.