Sampled Noise Amplitude
Another way of posing this question; most ΣΔ ADCs appear to specify a
  peak-to-peak input-referred noise for a single measurement under
  various conditions (e.g filter mode, data rate, PGA gain, Vref, etc.).
  Given a known input noise spectrum as described above, how do I
  compute a noise amplitude to compare with the ADC input referred noise
  to know whether I can resolve my input noise in a given configuration?


The easiest way to do this is to call the 1/f noise flat


Source: https://www.edn.com/electronics-blogs/the-signal/4408242/1-f-Noise-the-flickering-candle-

Since we already know how to handle white noise sources, it's easier to work with them.
For example with this amplifier I would draw a line at 10e-6 from 0.1 to 10Hz



There isn't a way (currently) to mathematically sample a 1/f noise distribution mathematically. Why? because 1/f noise is more like a random walk, and the noise values now depend on the previous noise values.  A close approximation is to generate a white noise distribution and then filter it with a low pass filter. 

There are ways to simulate 1/f noise, and you could match up the amplitude, as described in this paper: 1/f noise: a pedagogical review.




  Figure 25: 1/f noise generated with the algorithm described in section
  10, amplitude vs. time(both linear scales and arbitrary units);
  starting from top, = 0, 1, 1.5 and 2.


Sourced: Figure 25 1/f noise: a pedagogical review.