Yes it absolutely matters. My brother was charged with three felonies in his only arrest, all of them dropped.

It shows up in his background report and no company has cared (or taken the time to notice) that they are dropped charges and not convictions.

He's basically treated like a felon and effectively got bumped out of his career.

Also, I've seen many job applications that ask a question like: "Have you ever been arrested for a crime, regardless of the outcome?" Presumably mere involvement with law enforcement (even if acquitted or charges dropped) is some kind of signal in these guys' risk formulas.