If I had a nanodegree and was listing it on my resume or mentioning it in job interviews, I'd be pretty upset if someone came in and deleted all proof that I had completed it.
Yeah, I'd definitely be pretty upset if someone wiped the record of my college degree, but (I hope) Udacity courses don't cost nearly as much as I had to pay.
Depend probabbly not, but "hey there is this thing this guy did" might be a real thing. Probably not weighted as much as other things but still relevant to some.
But if it's a simple "hey there's this thing this guy did", are they going to go to the trouble to actually verify with Udacity that the person took the course? Probably not.