Also would a 2200 SAT look better coming from a school with a SAT average score of 1400? Would colleges even know how bad the highschool is?
A 2200 SAT score is what it is. Many admissions committees have the ability to consider the quality of your HS as it evaluates the other aspects of your application.
My highschool’s school profile lists the average SAT score in the school.
Every HS sends a school profile with information such as the different levels of courses, average SAT, grade distribution etc. so your record will be reviewed in its proper context. You don’t get extra credit on your SAT score for going to a “bad” high school but the high score should give schools an assurance that you are ready to handle college level work.
2200 if your HS average is 1400 will obviously get noticed. Ask your GC to take a look at your HS profile and check whether the fact your school is lower-performing is indicated as well as % students on free/reduced lunch, plus, as relevant, % students whose native language is not English, % students who graduate, and among those who graduate % who join the military, attend a CC, attend a 4-year college (list of those), and any other indicators that would be relevant.
Also, check into Questbridge:
http://www.questbridge.org/for-students/ncm-national-college-match
Look for a poster named Jalaquan who was in a similar situation as yours and got into Amherst with a full ride. 