Even on a city free of private cars, you’d still share the road with pedestrians, other cyclists, and public transportation.
And even if you really don’t hurt someone else, it’s terribly hard on a bus driver if they kill someone, even when it wasn’t their fault (my wife saw this first hand when someone committed suicide by throwing themselves under a bus).
So no, if you drink, just walk, take public transportation, or get someone else to take you home, but don’t ride a bike.
(edit: typos)