If anything, I could see Uber being one of the first adopters of self-driving cars when they're ready. They're already investing in it heavily, hiring away 40 robotics researchers from CMU to focus on it. [1] They want to corner the market, get everyone using Uber, and then eventually make the change to self-driving vehicles when they're ready.
[1]: http://www.wsj.com/articles/is-uber-a-friend-or-foe-of-carne...