The Chiefs have made it clear they will take the best player available, regardless of position. Unless they pick in the top 2 or so, that will very rarely be a first round QB. Too many teams reach at the position. I wouldn't consider him as "dropping" either as there is no consensus that he is a top prospect, just that a QB needy team might gamble with him.
Basically, the Chiefs would have to think much higher of him than the Browns, Cowboys, Eagles, Rams, 49ers, Bills, Jets, and Texans as well as any other prospect on their draft board.