In the short term, yes, more cars will clog the streets but in a couple of years when people start to see autonomous cars as a real replacement for their cars, then car-ownership will go down and free up the streets. Then 1 car is for 10 or 20 people instead of 1 or 2 people. It will be better over time.
The question is whether these shared autonomous cars will remain clean and cheap. If they are not, then they just clog the streets and people still own their cars. On the other hand, the number of taxis would decrease, so it may become a wash.