I have left AMA and my insurance covered. I think if you wait 6-12 hours after the birth without problems, the drs will normally release you. At least here they will. I know many mothers, even mainstream mothers who had epidurals, etc. that have left 6-12 hours after a healthy birth.
I was prepared to fight when I left AMA for my insurance to pay. I contacted my attny before I left the hospital because I feared they would call CPS on me. My newborn was having terrible apnea. I took him to the pediatriican who advised us to do a 23 hour admit. When I got there. They told me I couldn't nurse for X amount of hours while they did some tests. By the 3rd hour I was hysterical. Then he started to cry, I gave him a pacifier and worked with him and fell back asleep but by the sixth hour I was going to nurse him come hell or high water.
They didnt like that one bit. They put him on a apnea machine and it was going off every few minutes because it was broke. This went on for several more hours. I was getting more and more upset and the DR never came to see us or would return my calls. I then got really agitated. My BP was high. I told them I was leaving AMA and the nurses that had been nice to me turned into total bitches. They told me I was risking my baby and that if I left the hospital he would die. I told them where to take their apnea machine and shove it where the sun doesnt shine. Add a few choice bad words. I had to sign my life away at that point to leave and have his security band cut off.
No one helped me at all. So I carried my ten pound baby, baby car seat, and huge diaper bag back to my car that was literally a mile from the room. I was not supposed to carry any thing over the weight of my baby due to have a csection. I was told right before I left that insurance would probably not pay if I left. I said I didnt give a shit.
They did pay. My pediatrician "fired" me. Like I was going back to her again. Now I have this real conservative old guy who has literally let me take the lead and has a cooperative relationship with me in the most conservative mainstream practice where I live. I did take my baby to that pediatrician the next day just in case CPS had been called on us.