Preparing for Graduate School as a High Schooler

Thanks! No, I have not been admitted to an Ivy League school yet or any of the universities that are on par with them. I am still waiting on their decision.
I just have one quick question about your answer to the first question. Suppose I did not find it absolutely necessary to seek a professor position at Harvard, Stanford, or any of these top tier schools, and would be content with some more or less average state school, would it be necessary that I have an Ivy League graduate education? Or would the amount of publications/citations/whatever matter more than this?