Cori is naturally immune to mind control effects, plus she's genre savvy enough not to do anything even adjacent to giving up her soul. I'm not sure how that immunity would work against the Dawn Machine, but I feel she'd be less vulnerable to it in general at least. Although I admit I'm potentially interested in a plot that involves getting someone's soul back from Letitia, and could offer Nathaniel up for it. Depending on how she couches it, I could see him potentially getting tricked into it, especially when he's more tired or in an emotionally vulnerable moment.