No, that's not how traffic works. That's like saying a pipe can flow an infinite amount of fluid when you used a liquid instead of a gas because you got rid of the empty space between particles.
Even with theoretically-perfect timing and control, the road still has a finite capacity because cars take up a certain amount of space, both stationary and moving (following distance is still a thing even with computer control because of the mechanical limitations of brake performance). Moreover, it isn't that much higher than we can manage with humans driving the vehicles already.
The only ways to exceed that limit are to make the vehicles smaller (e.g. bikes) or pack more people into them (e.g. buses or trains).




You're right: when traffic is at its critical density, that's often what triggers the shift from the free-flow regime to the congested regime. But just because you make computers drive the cars -- even assuming they did it perfectly without randomly braking, which they don't -- that doesn't mean it eliminates that flipping between regimes. At best, it might get you a little bit more capacity before hitting that critical threshold, but eventually it's still going to, and then something -- a squirrel darting into the road, a sunbeam glinting off something the wrong way and momentarily confusing the AI, a bump that disturbs the car just enough to make it slow down a fraction of a MPH, etc. -- is going to trigger that shift to the congested regime anyway.