That is an interesting question that can apply to almost any college regardless of how selective the school might be. It all boils down to a couple of factors. One , how active is the alumni in the school? Are they are member of the alumni association?
Are they members of any committees and do they contribute to the annual fund raiser/ Contributing money in the form od an annual donation is the how a college gauges a family or alumni's support and interest.
Having a son / daughter or grandchild apply is one thing and getting them in is another. Colleges are businesses and all businesses need capital to continue to operate. Alumni who contribute large sums of money have a powerful voice on campus, however, being a yearly supporter helps as well.
One way for you to judge how your school views alumni's children is to look at the colleges web site and look at the break down of the class 2018. Many schools have a detailed break down of the .class by admit status -- special interest, athletics, minority, alumni/legacy , etc.