Are you asking if Duke or JHU would give you merit because a state school gave you merit? No, they won’t care. They use their merit to target students that they want to poach away from ivy and ivy-like schools.
If you want to be a professor or go to med school, spending huge amounts of money for undergrad is just a terrible investment. Profs don’t get paid very well anymore…and med schools don’t care where you went to undergrad.