Answers: YES! Absolutely yes. Not only under the weather, but many cough medicine can cause you to hallucinate and lose a sense of actuality (and not in a cool trippy way- more within a "feel-like-you're-dying-and-don't-know-h... sort of way) if you drink a significant amount. People have died from overdosing on cough medicine. Gotta be careful, and with the sole purpose take the recommended dosage on those things.
Yes, specifically why they call it "too much".