Handling the firearm while drunk is certainly cause for revocation but in your new twist it is merely a presumption. If the gun was stored in the trunk he wouldn't be carrying so I don't see him getting jammed up criminally.
Another presumption you are making in this hypothetical is that he drove drunk. If it could be proven that he did so, and was convicted of OUI then he would be statutorily disqualified and could only be relieved of that disqualification after 5 years by going before the firearms licensing review board.
If the OUI was continued without a finding (CWOF) and he admitted to sufficient facts then that can be problematic with regards to suitability. However even the police report could be used as grounds for unsuitablility regardless of whether the case was dismissed.
