Bad, bad idea.
And who's to decide if any particular offense is relevant to a position for hire, the gate keepers of information???
From my own personal experience, I'd say it's relevant that a person is of a criminal mindset, period, no matter the nature of the offenses. I learned the hard way to avoid entanglement with my jailbird neighbors.
Old Welsh Proverb: "A man who would steal an egg will steal more."