Pulldown to prevent floating input pins for multiplexer
You cannot give a pull up or pull down resistor for the pins if they are supposed to be used by the user (by connecting to the ADC pin) The pull up value or pull down value will mess up the user inputs and give wrong values.   (However, a very high value of say 1 Mohms can be given. But it also depends on external circuitry what the user will be connecting and the internal impedance of the ADC of the arduino MCU)

It is okay to leave input pin(the 1:16 switch) floating.

Optionally you can give jumper options for the user to enable or disable pulldowns on your board when pins are not used.

Another point

You are using MCP23S08 chip which is an I2C IO expander. There is a possibility of enabling all the four 1:16 switch outputs. It means, there is a chance of 4 analog outputs from different units can be shorted together and may create a simple error to some serious damage to the sensors or other devices connected. Then that is a real concern.

I would use a simple 1:4 switch to solve this case. an extra IC still but worth the safety