I can confirm Bri's statement, the engine only runs when the vehicle is in high speed (I believe if it exceeds 30 mph), or if the battery needs to be charging - said charging is usually done while the Prius C is actively braking or passively decelerating, thus eliminating the need to be plugged in.
For those who are used to conventional gasoline engines, the change in sound can be quite disconcerting. My roommate accidentally left the key in the ignition - and the car still on - in the garage overnight after work. We are fortunate that the engine only ran when the battery ran low, and didn't when the battery was high - the interim time was enough to not cause CO poisoning. On the flipside, though, if he had heard the engine running, it would have been an auditory reminder.
The fact that the C doesn't have an engine sound in game adds to the realism (such as it is in the Simsverse), so I approve.
Source: Obviously, I own a Prius C
A blue one