Okay first, it depends on what they are feeling, you mentioned guilt and other feelings, that may play into whether they say yes or no. Is there more of a chance with more people? No. There's a term in psychology for that. As more people show up, less people are going to help you/volunteer(example in psychology is stranded on a country road vs highway, no one stops on a highway)

Now the car one, I don't know if they would be more likely to volunteer, only a moron would and I wouldn't volunteer, because I'd be waiting for the moron. You have a 50% chance of getting the car, but also a 50% chance of NOT getting the car.

Someone would be more likely to volunteer however, because no one's life is at stake.