Does delta-sigma ADC also reduce Gaussian noise on input signal to ADC or just quantization noise? The motive for posing this questions arises from a difference of analysis between a colleague an myself.

Our general environment is in the construction of an analog front-end which takes in signals to an instrumentation amp in the low microvolt range. followed by a gain stage which then feeds a 24 bit delta-sigma converter.

My understanding is that we can achieve a certain number of noise-free bits from the ADC, where the noise is the quantization noise. For any Gaussian noise on the input to ADC, this noise will not be reduced by the ADC itself. And in this regard, we need to do some additional averaging of the sampled data points for reducing the Gaussian noise as an additional processing step.

My colleague thinks that the delta-sigma ADC will also reduce the Gaussian noise on the input signal, and therefore additional averaging is not needed.

As a second question, is it the case that we should arrange the gain so that as much of the signal fills the dynamic range of the ADC so as to improve the SNR of the signal due to having a large signal quantized as a function of quantization noise. In other words, the quantization noise is a smaller fraction of the signal?

Could you help us out by commenting on this question?
No!  The ADC (delta sigma or not) can not reduce the uncertainty in the input.  It sounds to me that your friend has not made up a real signal flow diagram and then formed equations.  The answer to your second question is affirmative.  In fact it's generically  true that putting as much gain, without introducing extra, in the front end is a good idea.  But... think long and hard about input overloads distorting the signal and possibly overloading the amplifier circuit causing distortion and such; either in the front end amplifier or during subsequent signal processing.  In the "good"  old days overloading due to the input could cause numerous problems; including long term effects.  OTOH: detailed knowledge of the signal and noise spectral (or even time transient) characteristics can reveal ways to optimize your S/N .