Do people forget how to drive if there are no lights? I can't imagine many people would think "well, there are no lights, which means GREEEEEEEN!". Over here, a traffic light that doesn't work means it's now a stop sign.
That's still a recipe for massive gridlock as treating most traffic junctions as stop signs doesn't scale unless there are traffic cops to manually direct traffic
I've never seen a traffic cop but I've driven past maybe fifty or a hundred broken or shutoff traffic lights, mainly in our largest city and never got stuck. Local law states that you give cars coming from the right precedence and the crossing self organises around that.
I work in Barcelona and live in a town 20Km outside it. I drove back home just fine at around 16PM. Some traffic in the city, but manegable. My town has had electricity in homes since 15PM, some neighbourghs told me.
At night I drove to my parent's (different town, 10km away) since I couldn't communicate with them and was worried. Their town was pitch black. People were driving mostly safe and slowly. Of course you get the random POS that doesn't care, but I didn't feel in danger at any moment. My parents were fine. I drove back home later and same story.
I just woke up (it's 7AM here) and the Internet is back and I have a message from my parents, their electricity is back too.
Overall, I didn't see any crazy behaviour.