Katie has made some great points on AROM. I'd also add that you might consider GBS status in any decision made on AROM (if you are planning on having the testing done), as your baby is not exposed to this at all until after the membranes are ruptured, but once they are, what my midwife explained to me is that it takes four hours for the IV antibiotics to be fully effective in preventing possible illness to the baby. So, in a way, if those membranes are still intact, that is also a natural line of defence for your little one.
Congrats for considering AROM and your position on it early, however, because I'm sure there are many women who do not even think of this in their birth plans!
I had a natural birth and no Pitocin, so I cannot compare in any way, but I can tell you about my own personal experience with AROM. I was GBS positive, and planning a completely natural birth in an out-of-hospital birthing center, therefore the long discussion with my midwife about the risks/what course of action we should take on treatment. I chose to only have the midwives/assistants use a topical antibiotic during checks (I could have opted for IV antibiotics), and in the end, with the way everything went, that choice was perfectly fine for us, as I delivered a healthy, happy little girl less than 15 minutes after AROM. I did not feel that the membranes being intact impeded the actual progress of my labor in any way (although it might have slightly slowed down dilation of my cervix), but rather that it slowed the labor just to the point that it should have, allowing my body to get ready for the delivery of my baby. When I began to feel the urge to push, I actually pushed through about two contractions with my membranes intact, and that was when I did feel as though the membranes were an impediment, as I felt like the baby was bobbing all the way back up to the original position after each push, so it felt as if I were making absolutely no progress (I can't tell you if this is the actual case or only in part). The midwives said I was making some progress, but I don't really know if they were just trying to be encouraging.
I have read many studies that say there is no conclusive evidence that the tendency for your water to break is passed down genetically, but I had really kind of guessed that I might have thicker membranes because my mother had AROM with all three of her deliveries (really, just because that was what I was most knowledgeable about, and had never really been with a laboring woman who had ever just had her water break spontaneously!). My mother's hospital AROM was always done shortly after she arrived, just as a matter of practice. When she delivered me (her first), the doctor went home after the AROM assuming it would be morning before she delivered, and she delivered me I believe within 2 hours of arriving, so it may have helped to speed things along (she had also been inducing at home with castor oil and walking). With my oldest brother, it was around 4 to 5 hours after AROM when he arrived, so it's hard to say whether or not it sped things in any way or would just have been the natural progression. With my youngest brother, AROM did not seem to help in any way, and my mother still received Pitocin as she had a lengthy labor with him even after her waters were broken.