We have this in the UK and my understanding is if a car removes their plates or uses a plate which is invalid it will be flagged up and they will be inviting police attention.
Although, I think where this comes into play most is that in the UK our police cars are also fitted with the same technology so if a car has a valid plate which doesn't match their vehicle or simply has an fake plate they will be immediately pulled over, so you'd be kinda stupid if you were driving around frequently committing crimes with fake plates on.
I know that California's doesn't match plates to car make/model, at least the toll and red light cameras. Someone faked my friend's license plate on their car and he's been getting all their tickets. Their cars aren't even the same color.
I lived in the UK for 10x the time I've lived in San Francisco, but here in SF I've witnessed many more instances of cars driving with obscured plates or no plates at all.
I don't think the camera system is picking up that the plate doesn't match the car; more if the vehicle has been reported stolen, or doesn't have tax/MOT/insurance.
Although, I think where this comes into play most is that in the UK our police cars are also fitted with the same technology so if a car has a valid plate which doesn't match their vehicle or simply has an fake plate they will be immediately pulled over, so you'd be kinda stupid if you were driving around frequently committing crimes with fake plates on.