I always nursed when DD was swaddled, I cant imagine a reason not to. Sometimes swaddling helped her to focus on the boob and nothing but the boob. When we were in public and it was time.to.eat. and she just was way too preoccupied with her surroundings but I was becoming engorged my go to way to nurse was to swaddle her up and throw on a nursing cover. That was is was just babys face, mommys boob, and mommys face. I imagine there are tons of women who do this. I never didnt nurse when she was swaddled. In fact, that is how she got to sleep many a night.
Oh and YES to the bolded. I had forgotten about that. I had really low supply so the baby had to work to get her milk. If she wasn't starving, sometimes she would rather look at her fingers or touch my hair and get lost in doing that. Which, for moms with good supply wasn't a problem.....but my baby kinda needed to sustain her latch with me and if she didn't, she'd likely as not lose interest. Swaddling REALLY helped us with breastfeeding.