The varieties I'm growing are not listed as being parthenocarpic. But they are ones that tend to have a strong tendency to set fruits without pollination. I don't know if the little squashes would continue to grow into large fruits, but as long as I'm getting baby gourmet squash I'm very happy.
So far it looks like I'm getting around 80% of the female blossoms successfully producing fruits. Yes, I'm seeing some aborts. I'm not attempting to pollinate the flowers myself. If I even just get two thirds of the flowers producing squash, I'll be very satisfied....especially if that means no additional work for me. If the percentage falls below 50%, then I'll make the effort to hand pollinate.