Legal Question in Criminal Law in Arizona

No, not if the employer does a background check. You could try to have the past conviction expunged which, depending on the nature of the employer and the questions they ask you, would help but not necessarily guarantee the employer would not learn of the conviction. As for your second question, yes it "might" be possible, but in the end - from both a legal and practical standpoint - it depends on the circumstances, most importantly, the particular charge you were convicted of (for example, a conviction for a "dangerous offense" would forever disqualify you). You can contact me directly if you want to explore further and provide more background.