Suitability issue for public trust?

Question. In January while going to lunch I hit a gate where I work around 130 in the afternoon while going to lunch. No damage to my car or gate. They sent me for a breathalyzer where they detected alcohol was in my system but I was not legally intoxicated. It was a monday and the day before I was watching football and having drinks. I left the party at 10. I was suspended for a week because I was told by the urgent care calculated I was legally intoxicated when I clocked in at 7 although I saw no paperwork to that affect. The terminal manager lectured me and suspended for one week. This was a one time incident. I onboard the 24th for a public trust position. Thoughts, will this be an issue for suitability since I will be completely honest during the background. Would it be enough to terminate me once I’m already working since I’ll be on probation. Thanks.