Nothing counts 'til you have the badge . . . If you have already had a DUI, it's difficult but not impossible to get hired. A candidate who seldom drinks was stopped after his wedding reception. You could try and get the record expunged. You should never bring this situation up in an oral interview unless the panel does.
Many candidates feel they have to do repair work.
It will only bury you. The panel probably won't because this is something that is handled with the background investigator. All the background investigator is looking for is a reasonable explanation of what happened. If not, it can be considered an isolated incident. He had been testing for five years.