Yes and elite college brand has an impact to many hiring managers. However, it is really the combination of college and major that is important, with major being primary and elite college brand being secondary. From an economic perspective, for those of us who are not born to wealthy families, and you will have given your child a much better chance to succeed financially.
There is no question that the going to a school that is higher on the ratings continuum and picking a more useful major will both open more doors for you. If you choose a full ride to top 200 school like Ball State University (for example) and major in PE over a top 10 college like Penn with an engineering or business degree, on average, the jobs available to you at graduation will not be as high paying and there will be many jobs that will not be available to you.
That does not mean that you will not have a great career or be happy, and there are many cases where the BSU PE major will do better financially, but not on average. However, there is a lot more to life than financial well-being.
Futhermore, there is a real continuum of colleges, and a real continuum of majors, and it is important that a student feels at home and comfortable with the school and major they choose.
It is also clear that the impact of selecting a good major and college on the rest of your life, is greater for families in the middle and low end of the income spectrum. If the student choosing a Ball State PE major over Penn Engineering is one of Donald Trump’s sons, then I think the opportunity cost of choosing the easier path is a lot less. The wealthy can overcome this a lot more easily than a poor, first generation, URM.
Additionally, a significant part of being able to monetize the elite college brand is really related to opportunities you can access and take advantage of. For example, it is not just that the Penn engineering student is attending Penn, but also that they are much more likely to have had to opportunity to construct a more impressive resume. They may have been able to spend a summer at MIT, or work as a research assistant to a Wharton or Engineering professor and have their name on a couple of published research papers, or obtain an internship with a company whose name is widely recognizable, and have more connections to people in positions of power. Bit by bit, they are changing something abstract (college brand) into real knowledge and experiences that they can more specifically quantified and explained and create real advantages when competing for jobs.