The core issue with this question rests in probability. Specifically:
What if a kid is crossing the street and avoiding it would kill the driver?
How does the AI know for certain that avoiding it would kill the driver?
and certainty rears its head re:
1) If a dog is crossing the road, I'd expect the car to try to avoid it. But what if this leads to .00001% more risk for the driver? What is the 'risk cut-off'?
There would likely be no "hard cutoff". Earlier fuzzy logic systems have been implemented in automotive gear shifting and anti-lock breaking, but it is precisely the "fuzziness" that made them effective. Contemporary AI is far more sophisticated, and part of that sophistication rests in what might be though of as dynamic thresholds for decision-making. Because certainty only exists in special, limited cases (such as solved games), estimation must be used.
Regarding the cockroach, it would likely be too small to warrant a response, although a swarm of cicadas might affect the car's sensing ability and prompt poor-visibility navigational protocols. In general I'm sure pet-sized animals and bigger would be avoided, in the case of actual pets for humanitarian reasons, and for animals like deer, for reasons of driver risk (impaled by the horns at the worst, and at the least potentially costly damage to the vehicle.)
But I suspect the protocols for this would be breaking or swerving if there is a clear margin on either side of the animal (i.e. not a barrier, wall or cliff) and the direction change is controllable (i.e. hitting the animal is likely to result in less harm than an actual crash, and certainly less risk to the human, except in the case of the deer's horns.)