As a Fuck-You-I-Won't-Do-What-You-Tell-Me type, and a rabble rouser even while I was in high school, I'd have organized a student boycott of football games just on principle, and I would have kept it up until they stopped this foolishness.
And I never once tried going to a HS football game with alcohol on me or ingested. But I object to this kind of invasion of privacy, particularly if innocent.
EDIT: Also, what Zorg said. Too many false positives, and this would do absolutely zero to curb or reduce teen drinking.