So, if I were hiring a candidate, would a Udacity Nanodegree weigh in their favor? Absolutely. Would I hire them if they had no other formal credentials at all? Absolutely, depending on all of the other factors. But as for that matter, you can ask me "would you hire somebody with no formal credentials at all" and the answer is still "absolutely, depending on all of the other factors".
I don't know where you're based right now, but I'd say most recruiters across the world wouldn't understand the concept of a Udacity nanodegree. Most of them don't understand that you really don't need a piece of paper stating that you can write code; recruiters simply don't understand that it doesn't matter whether the person is even a graduate or not, if s/he can write code.
I'd just tell the person to keep trying. I kept trying, and I got lucky with a media house that was okay with hiring me to write code without a relevant degree or experience. I'm sure I can't be the only one to get lucky.
TL;DR - "Natural affinity" should include some level of skill/competence, plus that glint in the other person's eye when you talk about writing efficient, beautiful code.
Within the population of programming jobs, some are actually pretty serious, actually require solid CS basis and a scientific approach. If I was hiring for that sort of job, Id look for higher degrees and experience. Similarly with data science type stuff. When it gets hard, you need the right background.