I doubt it as the promotion exams are simply to go over to the 2nd year. I say simply, but this is again one of those milestones in Tootsuki meant to separate the gifted few from the masses. They already explained the ways how you can obtain a seat: either you win it via a Shokugeki or the Elite 10 Review Committee will scout you. Logically when an E10 member graduates, the committee will first look at the students who excelled at the Autumn Election among others, but I don't think you directly will end up obtaining a seat just by going a year higher. Unless there's a third way to obtain a seat, but I reckon there are a bit too many options for this to work efficiently. Of course it's possible that Azami is going to tweak this year's promotion exams.