I don’t know the international student rules and visas, as to what happens when a student turns 18 or graduates from college. Also don’t know how the two year/graduate from high school rule is enforced by SUNYs for document vs undocumented students. THese are all questions the OP needs to investigate. S/he will be here in two year.
I CAN say that most every single person I know who went for a green card, did NOT get one in the expected time frame. Something always came up, so waiting for one is not something I think is something to count on.