Perhaps that's just another urban legend, but my gut says no.
I have witness this on two different occasions. Mother always chose the life of the baby over her own. By the way, both mother and child survived in both instances.
My daughter was in that situation, fortunately she and the baby survived.
He was born early and today at six is healthy, energetic and happy, she is happily tired.
Well, that’s the natural maternal instinct, but it isn’t universal, even in humans. Unfortunately.
Also, as humans, we have the ability to override our instincts pretty easily, for good or for bad.