FFT Affected by Other Inputs

When running an FFT in a signal from analog input A0, will reading from other analog inputs (not FFT) at the same time cause issues with the FFT?
If so...

1. Will they be predictable i.e. only FFT sampling rate changes due to servicing the other inputs, so results are different but usable?
2. Will they be unpredictable i.e. FFT results are garbage and no way to fix them?

I want to simultaneously evaluate one input signal with FFT and the output of several filters.

All the analog ports use the same ADC so readings will definitely affect each other.

An often used strategy is to read a port twice and only use the second one as most interference will be in the first reading...

the same ADC so readings will definitely affect each other

It's not a given it depends on the impedance of your audio output. What is your circuit like?

For the circuit, there's a bank of active filters to A1 thru A6 analog inputs and an anti-alias filter to A0. The filters have peak detector circuits on their outputs, and the hold-cap discharge resistor (output to ground) is currently 100K (probably should make smaller). The anti-alias has no peak detector.

Why do the analog inputs affect each other? Even with one ADC, it's likely multiplexed to each input, isn't it, or does it use a resistive network perhaps?

Why do the analog inputs affect each other?

Because inside the arduino there is only one A/D converter and the various inputs are switched to this. If the impedance of the input voltage source is too high then there is not enough time transfer the input voltage to the sample and hold capacitor, so the reading is dependent on the previous reading to some extent.
Ways round it are:-

1. reduce the output impedance of your source.
2. Take two readings on the same channel one after the other and only use the second one. (this gives it more time to acquire the charge)
3. Take two readings on the same channel one after the other with a delay in between and only use the second one.