Yes, studies show that c-sections delay the milk.
I had plenty of milk after my 3 c-secs, but I failed at breastfeeding my first 2 c-sec babies simply due to the pain factor. I just could not get through the early weeks of painful nipples and engorgement while I was dealing with so much pain from my surgical recoveries. By the 3rd baby (also c-sec), I was determined to have a successful breastfeeding relationship, even if that meant crawling through broken glass...and it was nearly that painful, but we did it, and I nursed her for 2 years. After my 4th baby, born normally, breastfeeding was still challenging with engorgement and painful nipples, but I wasn't deterred at all, because I had basically no physical recovery after my very easy vaginal delivery.