You know this subject seems to be coming up more often now than before. Although I can't answer the OP question in terms of being hired by a regional or a major airline, I will offer you some advice from personal experience.
If the DUI conviction occured prior to them getting their medical, then obviously they have been cleared by the Office of Aerospace Medicine in Washington DC or OKC to fly airplanes. Just as others have stated, be honest and transparent about the situation(s) when questioned about it.
Tell your buddy to set themselves apart from the rest of the applicants/class. Once the Feds give you the green light, everything else is about timing.
All the best to your friend.
atp