I wouldn’t count on that. An inferior public school will not be able to get kids into top colleges because the curriculum isn’t as challenging as other places and colleges know that plus they look at previously accepted students to determine performance of future kids from the school. So if the kids that went before struggled, then a college will not admit any more kids. Some public schools just can’t get kids into the top-notch schools.
For example, for a while, my parents interviewed kids from the best public school in Albuquerque for their alma-mater. They gave up after 10 years of doing this because NO ONE AT ALL EVER got accepted from the public school even when my parents highly recommended them. If you didn’t go to a certain private schools in New Mexico, you just couldn’t get in to their Alma Mater.
I’ve also known someone who was valedictorian at his school (in NM) who applied to MIT and was turned down. His school was simply not of the caliber to admit kids (I feel bad saying this, but realizing that he was a white male who hadn’t had Calculus, I understood that he didn’t stand a chance, but if he was valedictorian, no one else probably stood a chance either).
There is one exception to this which is that whatever your school offers, you are expected to take much of it. If they offer 20 APs, you need to take a lot of them. If they offer 4 years of a language, you need to have 4 years of a language. You only get a pass on some of these things if your school doesn’t offer them.