As long as human drivers are still in the mix, no, self-driving cars will not solve congestions. But fully self-driving cars could improve road efficiency by an order of magnitude. There is no need for trafic lights, they can drive in very close formation, they don't need parking space nor search for parking.
Additionally, an inherently safe trafic system doesn't require 2 tons of steel around you for protection. The car can be stripped down massively reducing road footprint and ecological impact. You will also hail the smallest (cheapest) vehicle that serves your purporse, a single commuter can comfortably travel in a bumpercar.
I'd be curious what percentage of congestion is caused by accidents, which one would expect to substantially decrease in rate with autonomous electric cars (fewer impacts & maintenance issues).
Additionally, an inherently safe trafic system doesn't require 2 tons of steel around you for protection. The car can be stripped down massively reducing road footprint and ecological impact. You will also hail the smallest (cheapest) vehicle that serves your purporse, a single commuter can comfortably travel in a bumpercar.