If I use a biasing circuit for a signal going into an analog input pin, will it affect the ADC operation?
It will give bad results. You're not slowing down the sampling, you're taking samples at a longer interval - a very different thing.

The Arduino uses a Successive Approximation ADC. That uses a clock to control the output of a DAC and compare that voltage with the incoming voltage stored in the S&amp;H capacitor. 

In order for the S&amp;H capacitor to get charged to the correct level it has to be connected to the GPIO pin long enough. Since there is only one ADC and 6 analog input pins, it goes through a MUX first.

The delay that needs increasing is the delay between the pin being connected to the capacitor and the capacitor being connected to the ADC.  This is called the acquisition time.

The analogRead() function does these basic operations in sequence:


Connect the SHC to the GPIO pin through the mux.
Wait
Disconnect the SHC from the GPIO and connect it to the ADC
Clock each bit from the comparator to the result registers.


Putting a delay between each analogRead would just delay the connecting of the SHC to the GPIO pin, not increase the time it's connected to the GPIO pin.

You would have to manipulate the ADC registers to do your own sample timing.  Or, just reduce your output impedance.