In short, the answer is yes. Physiologically, orgasm is a reflex generated from effective stimulation. What initiates orgasm for women is the pubococcygeal muscle, a cluster of striated muscles that holds the genitals together. If you think about childbirth, the baby passes through this muscle band on its way through the birth canal. In addition, labor releases prolactin, oxytocin and other beta-endorphins— the same hormones released upon sexual pleasure and orgasm.
While orgasmic childbirth is not common in our culture, Dr. Christiane Northrup claims this might be because we are ingrained with the idea that childbirth is a medical emergency that can be dangerous and painful, rather than natural and intimate.
However, the majority of women who have undergone a vaginal delivery, and in particular without an epidural, attest to enormous pain. But even if your tolerance for pain is high, pain in general can inhibit orgasm.
Alternatively, some women may fear having an orgasm during childbirth because they find such an expression to be inappropriate. Sexual pleasure is often not a permissible emotion to express in our society, particularly in public. However, you may want to consider that if you had an orgasm making the baby, why is it not permissible to have one while delivering it? Perhaps having an orgasm in front of your delivery staff seems more embarrassing than screaming angry curse words? Remember that orgasm is not something you can achieve or make someone have. Orgasm is about letting go and surrendering to your highest pleasure potential. To surrender to yourself, your partner, and/or the experience, you need trust and the ability to be vulnerable. Thus, surrendering to labor, especially with your first baby, can be very scary as you are most likely encountering many unknowns.
If you are interested in having an orgasmic childbirth, you may want to consider where you deliver and who supports you and the process. You may also want to watch the documentary Orgasmic Childbirth to see how other couples have approached childbirth and surrendered to the potential of an intimate birthing experience.