Short answer-No, she comes out the (somewhat) normal way...
Long answer- No, she comes out through the normal birthing process, however, because she is part vampire things were different. I.E. The placenta (being as hard as stone) cracked open, and on her way out Renesmee broke many of Bella's ribs as well as severed her spine.
No Reneseme does not eat through Bella. But, Edward had to bit through the womb because it was like vampire skin. It was the vampire version of a C-section.
Vampire Caersean 8D