Yes to a point breed or more so genetics play a role in hatch-ability just the same as nutrition. Most all my birds are purebred and I have a closed flock, my Rhode Island Reds have been line bred for close to 10 years now.Another variable to consider is the breed of the chicken. I've found that hybrids are insanely easy to hatch while some of the purebred strains are more difficult, possibly due to inbreeding with the more rare varieties. For a true test, I imagine you'd have to split the same genetic pool into groups and keep the other conditions the same as well, other than the feed. I'm not looking for the results of a big study.....just a general impression from fellow poultry hobbyists. Nutrition is an interesting subject.
I keep my protein at 18 to 22 percent protein and the protein in the feed is both plant and animal based, along with the amount and type of protein vitamins and minerals also play a key role also.
Chris