Shared vehicles don't need to be parked between rides, and sit idle much less between rides. The former doesn't really impact anything unless shared vehicles are common enough to impact city design. The latter doesn't impact anything unless there is a marginal capital improvement to the vehicle that only pays off if the duty cycle ratio is high enough. I don't know of any such technology off hand. Bypass oil filters with full-synthetic lubricant, perhaps? Season-specific tires? Special paint job that reflects all non-visible light? Hybrid with regenerative brakes? They all seem to me like long shots at producing an actual effect on emissions under real-world driving conditions.
If anything, I'd think that shared vehicles could increase emissions, because the vehicle has to travel between the site of one ride's end and the next ride's beginning. That travel does not accomplish a goal of getting a rider from their origin to their destination. The inter-ride travel is minimized in a denser city, but those cities can make mass transit pay off more easily, for the same reason. In a dense city, the strongly overlapping trips can be coerced onto common routes with fixed stops. So the shared vehicle probably does not save emissions unless the trips of multiple passengers can be easily combined. And if they can, just put a bus route there.