It did with me (granted, N=1). I reduced my own driving to zero and replaced it mostly with Uber. That isn't just a shift in my quantity of rides demanded, it's a shift in my demand curve.
> driving cars is unskilled labor
I would not have given up driving if the alternative were yellow cabs. New York taxi drivers are not knowledgeable about routes. Further, it is not uncommon for a trip to end with a debate over whether the credit card reader works. I will pay extra for even a minimally professional Uber driver over an unprofessional yellow taxi.
The correlation between driver skill and rider experience is one of the problems Uber is running into when it considers scaling. That limitation is one that would be mitigated by driverless cars.
> The drivers will go elsewhere, not find other jobs
Network effects limit the viability of alternatives: there will be less demand on those platforms. As mentioned above, I do not believe most yellow taxi drivers would do well as Uber drivers–the supply is not fungible.