I'd find it very surprising if it worked. Here in Costa Rica you often drive inches from other cars while dodging potholes and other obstacles in the road, and I can tell you now that the relative anarchy is not any better. They have one of the highest traffic mortality rates on earth here, and are just now starting to crack down. They have roundabouts here, which are like an intersection with no lights and it just makes traffic worse once you get a certain amount of traffic. When they are replaced with overpasses and traffic lights things improve. Otherwise there are huge traffic jams behind each roundabout in rush hour.
And in other countries it's worse, in Panama nobody pays any
attention to the traffic lights, and quite frankly it was a horrid experience that was enough to ruin an otherwise interesting city for me. The traffic is insane, with everyone trying to get through the intersections at once and driving like absolute maniacs, up sidewalks, going the wrong way to make shortcuts, it's just awful, I sat for hours and hours in traffic in Panama just because they didn't respect the concept of taking turns at an intersection and tried to all go through at the same time. Recently they made international headlines when a bunch of people on a bus were killed in an accident with a truck, and I have to say that based on my experience there it wasn't very surprising.
I think it would take a very polite culture to pull it off, because whenever I see anarchy on the road, it ends up very literally being every man for himself with nobody wanting to cede an inch.