There are no 'unused' analog inputs unless YOU specifically set the pin to be an analog input and then try and read from it.
If you take a 'mega' for example, then there is only ONE ADC. YES - ONE.
That is it.
The 16 supposed channels are not 16 ADC units, it is just the one ADC unit along with a 16 input multiplexer..
The mux is only ever set when the pin is called for a read hence the only 'unused' analog inputs are in your mind.
If you want to set the built in input pullups on an unused input then that is fine. Problems with noise will tend to be in your code, or as said, by you not following the correct practices and parameters as described in the datasheet for ADC use.
All the information you need is in there.