I agree largely with Tetradon. To answer the question, yes, it does matter where you went to school. For the last several years, I have been part of the hiring committee, we need engineers, data/computer/information scientists, financial specialists/accounting types for our consulting practice. So for starters, a grad will have to have marketable skill, preferably engineering and comp sci. For Big 10 schools, we largely look at UofI and Purdue, and maybe Michigan. We compete more for Stanford, Cal Tech, UofCal, MIT, than say Uchicago or Northwestern. For Ivy we look at more Cornell and Princeton than Yale and Harvard. For grads with Liberal Arts degrees, you better show something great on your resume and damn well show some aptitude on the various rounds of interviews to make it in here. We do take plenty of laterals, but 5 years solid (10 preferred) work experience to make associate, but unless you know someone who works here as a reference, a school like e.g. Indiana State will likely ding the potential lateral out of the hiring process.
As for centi-millionaires, one thing that gets bandied about around work here is that millionaires -- not centi- -- are often self-made and something like 3-5% are millionaires from inheritance. The drive to create and move/innovate business is the key to consulting and is something that is largely pushed and highly rewarded. To get to the centi level, from what I see, you have to own your own business(es). These people are largely from the schools mentioned in the OP. They need labor or other like minds to pull of their business plan. I agree "learning" from college is somewhat overrated, but the connections one can make to realize these opportunities is one of the largest reasons to go to such a college in the first place.