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comment/ator
The major source of concern is that you had both a DUI some time ago, which isn't necessarily a reflection of your current lifestyle and habits, AND a more recent one, which absolutely may reflect upon your current habits and situation and your supervisors may believe will be reflected in your work performance. And two DUI's is getting over into the land where nothing is funny. It hints at a problem here beyond simply choosing not to drive after drinking.
If you have in any way discussed what has happened in the last year with any of your co workers, you can just about rest assured that it will come up if you apply for and are in line to receive a promotion. If you have spent any time away from work with co workers and they know you to be a hard partying individual, this may come up. Your supervisors likely already know some things. Unless you have significant life changes to report to them at this point other than you're worried about the MVR check, I'd wait until the issue comes up, if it does, since you didn't inform anyone all those months ago.
Check your company's policies regarding your responsibility to inform them if you have any brushes with the legal system. Some have this detailed in their handbook. You could very well be terminated, without illegality or even much potential for unemployment insurance if you did not inform them and you were supposed to, and they discover it through a check at this point.
No, you have no legal recourse if the company doesn't give you a promotion based on your MVR because I am sure there are other candidates for the promotion. They will not likely be dumb enough to tell you why you were not the chosen candidate, they have no responsibility to tell you specifically why you not given a promotion, and there's no law protecting you as a person with DUI's As far as a termination, you'd have to wait until it happened, and then look at the specific reason why you were terminated. Above all, do not make it because you engaged in a battle with them over whether or not they can discriminate against you or not promote you because of the MVR. You will not win that one.