No it's not a drug. I could be wrong, but I'm pretty sure the distinction is that it doesn't produce a psychoactive effect in the same way a drug does. Like, pathological obesity doesn't mean you're addicted to sugar, it means you're addicted to food for one reason or another.
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I've swen a kid bite an ear off because he was on a sugar high before that he had staright As and was overall a perfect student