In my experience a Master's/Bachelor's/PhD might get you into the interview room because of your resume or recruiters coming to campus, but in my experience I've been disappointed about the knowledge gaps in recent graduates from well-known schools. I've also interviewed Masters/PhDs who studied my field, but were interviewing for user-facing support roles when they're clearly better suited for something more focused on r&d. Or they've focused so much on a specific subset, they're lacking the general knowledge needed for that job. IMHO, degrees don't guarantee anything for me. At most, they're a jumping off point for how your interests and background apply to that job.
More important than the degree are the projects you've worked on, your role in them, and challenges you've overcome. You could take the nanodegree and omit it from your resume, but put the projects on there as personal projects. Just don't misrepresent your work. It can be a surprisingly small industry. Someone might recognize a project as something they saw online, or know someone who worked on it.