I am not sure if orgasm is possible, but like Kotchanski suggested, perhaps if it does happen the woman might feel shamed into silence or pressured to agree with the dominant "birth is torture" viewpoint.
Regarding an aspect of pleasure during childbirth. A few years ago, Susie Bright wrote articles about the "sexual side of birth" and her experience with a vibrator as labor aid. One of her few defenders was Betty Dodson, which is where I initially read about it, but she received a lot of negative feedback for associating birth with pleasure - even as pain relief. I'll post an excerpt here and a link to the rest -
Susie Bright's Journal : Egg Sex
"I pestered my teacher for three weeks about whether she thought using a vibrator during labor would be helpful for pain relief. She said each time that we would discuss it next week. She recommended all sorts of other distractions and exercises: going to the bathroom frequently, changing positions, getting in the bathtub, focusing on a special object, etc. Well, I decided on my own that my Hitachi magic wand was going to be my focus object. I believed that stimulating my clit would be a nice counterpoint to the contractions going on inside my belly.
I have a great photograph of me in the delivery room, dilated to six centimeters, with a blissful look on my face and my vibrator nestled against my pubic bone. I had no thought of climaxing, but the pleasure of the rhythm on my clit was like sweet icing on top of the deep, thick contractions in my womb. [...] Due to my baby's unusual breech position, I had a complicated birth that finally ended in an emergency Cesarean. But I had a great labor."