"hmmm",
connect a 1F cap and you get the pot change after a minute (like DC). OK, it will look "rock-solid".
The resolution of the ADC is a different topic: there are non-linearities, there can be noise (from VDD, from AVDD). It is not related to any cap. With a cap connected you just "hide'" (filter) the noise (and non-linearity).
Many ADC specifications come with an information how accurate the LSB can be: I have seen ADC where 2bit LSB are in the range of "uncertainties" and these are still considered as "pretty good".
What do you mean by "how good is the resolution below the LSB ..." You want to measure in half-bit resolutions?
You want to measure in "fractional bits"? How to do (when LSB is already "flaky").
And what is "ADC of this type need a low input impedance, for the sampling time,..."?:
If your ADC has a low input "impedance" (or do you mean "resistance") - it would shorten your circuit which you want to measure: with a perfect impedance match, e.g. 50Ohm source and 50Ohm ADC input impedance - you have a voltage divider, resulting in 1/2 of source voltage - right? (and just for a specific frequency)
And "impedance" is frequency dependent! If you add a cap, you make the "impedance" much smaller"! Now all your high frequencies, e.g. noise, EMI, RF signal interference (and also noise via the power supply) are "rejected" (filtered).
The "correctness" of the LSB of an ADC is also a function of temperature drifts (of all your components involved).
Simple math:
Let's assume you have a 12bit ADC: 12bits a 6dB gives you a "possible" resolution of 72dB. If you use LDOs, SMPS with 60dB PSRR - you get still 12dB "ripples" from PSU into your analog signal. So, 12dB / 6dB are already 2 bits (LSBs) as "noise" (uncertainty).
Good luck. to "compete with physics". LOL
