I'm afraid things more complicated, than simple noise math equations. Since we have switched capacitor load for voltage reference, output impedance of the voltage reference may have more importance than noise level itself.
In the middle frequency range ~ 1 kHz, where capacitor 47 uF have R-react. = 3.3 Ohm and doesn't help much with settling time, likely inter-modulation / interaction processes would happened, so ADC turns into noise generator as well.
I see TI starts to characterise REF61xx specifically for this case - sourcing high resolution / high speed SAR ADC.
Zenner as a voltage reference, shunt TL431, another series, slow / weakly buffered references may be wrong type in this case, despite how low noise level they may have.
And it also imply, noise tests for ADC with shorted inputs dumb stupid things, well, at least for high speed SAR ADC.
Have to ask AD for FFT plot clarification.