It all depends which country & which are you going to be flying.
Most of the airlines in lesser developed world would care less about DUI, speeding/ Traffic tickets & nor can they find out.
Mostly all they care in an EXPAT is accident / Incident free flying history, time on type.......
Still, it won't be a bad idea to check with a pilot flying with any such company.
Don't dis-qualify yourself by over disclosing..... The rest of the world doesn't work like USA.....