Not in my lifetime... or yours, probably
Wilful interference aside I simply don't see the concept of autonomous cars working, at least not without a great deal of "upgrade" to road systems. Given there could not be a "big bang" changeover between conventional and autonomous vehicles, there would be a long period (possibly infinitely long) where the two had to coexist. Then think of traffic lights; if my autonomous car is approaching lights at red and there is a stationary car ahead of me then my car will stop. (I hope!) If, however, there is no car ahead of me how will it know (a) that there are traffic lights there, and (b) that they are on red; put simply it won't unless there is data being permanently fed to the vehicle about what is ahead; "lights ahead" _could_ be incorporated into an in - vehicle mapping system + GPS, but the state of the lights won't be. Note that we cannot dispense with the lights because of legacy, i.e. non - autonomous vehicles on the road. Of course the "lights ahead" information has to include some sort of algorithm to deal with the lights being out of action.
Now we come to a roundabout; I must give way to traffic approaching from my right, so my car has to have some means of detecting such traffic in the "relevant" place to know it must wait. Fine; now I am driving (or my car is!) in lane 2 of a motorway, and it detects a vehicle coming up to overtake me in lane 3; how does it know I am not somewhere in a roundabout and do something which might be correct at a roundabout but which would be downright silly on a motorway.
Or does it suddenly throw up its virtual hands, announce "does not compute captain" and cede control to me with zero warning. Now get out of that big boy...
Some of the potential problems might well be soluble with data fed more or less continuously to my car from roadside systems, but the same datastream has to go to other vehicles to which any given bit of data may be not just irrelevant but actively incorrect.
At the centre of all this will be a big in - car display which is less likely to read "Don't Panic" in big friendly letters than it is to read "Prepare To Meet Thy Doom". If you're very lucky you might just be able to absorb the true horror of the situation before it's lights out.
Some of the above may sound a bit facetious, but I invite you to think about it. It is meant in all seriousness.