As much as I would like it to be otherwise, signaling (namedropping of famous universities, companies, and people) works a lot. I guess mostly because people prefer to delegate decision making. The backside of that is that unless you finished (or dropped out) from a well-respected univ., you have an uphill battle of proving one's worth.
Though the ones who set "oh, you were at MIT" didn't know about this program.
* I think less than 1% of the high school students in this country (the US) are aware of summer programs such as RSI. Knowing about RSI, let alone being selected into it, is a strong signal that in your pre-college years you were very invested in math and STEM.
* even if you don't have a very prestigious college degree is not a negative signal anymore from my point of view. At 17-18 we are all very fragile beings (and we keep being fragile until at least 25), so lots of things could explain why you didn't get into a top university. I would inquire about that, but I would expect to hear some reasonable explanation (and I wouldn't mind if you simply told me it's personal and you don't feel comfortable going into those details).
* I would ask you if you participated in any math or CS competitions in high school/ college.
From here, lots of ways to have a pleasant chat for about 30 minutes.
When it comes to signals, I like your approach for looking at them as hints, rather than judgments.
You definitely don't need all A && B && C.
Sometimes being like-able and knowing someone is enough.
I'd say to get hired, you just need to convince the employer of your personality, current skill, and potential.
If that's the case, and someone's trying to hire you because someone they trust thinks you can get the job done, the question is whether or not a nanodegree can allow your interviewer to check a box for "has training in X" that will make the difference in sliding your resume past HR's desk.
A) your overall resume is impressive
B) you either have a portfolio of things you've built, or else you agree to do a take home assignment and successfully complete it
C) you can pass both technical and non-technical interviews
To get hired you need A && B && C. Doing Udacity will probably help with each of those things, but no one is ever going to hire you because of an academic credential alone.