The overhangs are in the model but not quite big. And yes it curls up, I know that this can cause collisions. For this particular model I printed without support since the overhangs are quite small and the head stays within the printed area. I saw that when it leaves the model to print the support outside , that when it moves back it can knock over the print.
But the position where the head strikes the print is way above any overhang edges, so that shouldn't pose any problems. The rest of the model is printed just perfect up to the point where it did what it did.
I can attach the model for someone to test as well if you'd like.