One bird in Missouri, this stupid Red Winged Blackbird, did not. In fact, it flew right into my path so quickly that I could not respond in time to avoid it. Although I quickly applied my brakes, I heard it bump against some portion from under my car. I don't think I actually ran over it, per se, because I didn't see any remnant left on my car. It likely just bumped into my car, and got knocked about. I didn't see it on the road behind, so I'm guessing it was able to fly off.
Still, it was very annoying. It's bad enough having all these birds rush in front of you all the time, but actually hitting them just sucks.