It will all depend how they get used
Its not just the potential computing power needed for self driving - a lot of that is happening anyway for additional reasons, but how usage affects overall mileage driven will have a big effect on the overall impact.
Many people point out that a personally owned car is very inefficient, and in one respect they are correct - my car is expensive in terms of resources and money to buy, but spends the vast majority of its time sitting idle outside my house or in a car park somewhere - a very inefficient use of an expensive resource.
But in another aspect my car is immensely efficient - virtually every journey it makes is a "useful" journey - taking me where I want, or need, to go. The only exception is once or twice a year when it has to make a short journey to a garage for new tyres or servicing - maybe 20 miles p.a. out of 20 thousand - that's 99.9% efficient.
One of the big arguments for self driving cars is replacing the personal ownership aspect with a more "efficient" shared style which makes better use of an expensive resource. But its worth noting that almost any form of shared usage, a traditional taxi, Uber, shared ownership whether traditional or driverless will result in a big increase in "useless" journeys - returning to base after dropping a passenger off, going to pick up a passenger, going between jobs. All this means extra mileage, extra fuel consumption (whether of the liquid dinosaur or busy electron variety) and extra road congestion. Now the more widespread the service the lower this useless journey overhead is, but it's never going to approach the 0.1% of the traditional ownership model.
Another aspect is if you have a personally owned vehicle capable of full service driving - how do you use it?. Obviously there are the standard usages - get work done during your commute to work, getting brought home legless from the pub. But there are other possibilities :- Don't want to pay more for your airport parking than the cost of your flight? - just send the car home again after dropping you off and then it can pick you up again on your return. Don't have parking handy near your city centre office or the restaurant you are going to - just send the car home - or maybe send it to find a free parking space out in the residential suburbs (very popular with the residents I'm sure). But this is all additional mileage, additional energy, additional congestion.
One other interesting question - how fast does a driverless car go when it's not in a hurry? - When I am driving or being driven I want to go as quickly as is commensurate with my comfort, safety and maintenance of my driving license - but if I'm say sending the car home after dropping me off somewhere I don't care if it takes 1 hour or 2 - whichever is cheaper in energy terms. We all know that 56 mph is a more fuel economic cruising speed on an motorway that 70 mph - how much better is 30mph? - that's going to cause fun!.