My last dd was born with the cord wrapped 4 times around the neck and 2 around the body. she was still moving positions until she stuck her arm out the birth canal and engaged her shoulder.
None of my others of my others were head down until right before they were born. As a matter of fact, at 41 1/2 weeks we were chasing Ds2 back into heads down position with the fetal NST I was having that day.
On the other hand, all my kids were born with the cord wrapped at least once around the neck.
I have done some research of cord wrapped or nuchal cord as they are called. From what I have read, about 25-33% of babies are born with the cord wrapped at least once, if not twice around the neck. Even if the cord is wrapped 4-6 times around the neck, there is no difference in outcomes between vaginal delivery and c/s delivery. The only thing I have found that a provider will not do is an ECV.
I don't remember where I found all the information as it has been 2 1/2 years since I did the research. I did the research because I was denied an ECV for multiple cord wrap, and told immediate c/s or dead baby by one OB. The other OB, the as I call him 'old school' OB was ok with letting me go into labor on my own and waiting to see if baby would turn on his/her own. At the time I went into labor I was breech, but a deliverable breech. She turned out of engagement, and tried to go heads down. But since my BOW broke on its own just a few minutes before, as she was turning, she got her hand in the birth canal and stuck it all the way out. She then kept turning and her shoulder became engaged. The only concern the OB had, when I went into labor, was that since she was breech and very high when my water broke the cord would prolapse.
As long as the cord is not being compressed, the baby is not deprived of oxygen.