Regionals fine.
But majors might have a higher standard, and might put more effort into researching your background.
The real question here is do you disclose it? Honesty is generally the best policy, because if you get caught lying you're probably done for good in 121.
But the nature of the infraction matters...public drunkeness in HS/college that long ago would be a non-event. Something like shoplifting would be more serious, but if you were very young and addressed it properly at the interview it would probably be OK.
Drug possession would probably be something you could get over. Drug dealing or any sort of violence would be a big deal if the employer found out about it.
If the issue is more serious, you might need to fall back on the letter of the law which may allow you to not discloses an expunged event. You have to make that call.
If at all possible, be honest. Better to lose an interview or two than get fired from a job after they find out.
Also...when applying to regionals keep in mind that some are wholly-owned or have flow agreements with majors. Anything you disclose or don't disclose could come to haunt you later, assuming WOs share info with their major partner.