Does "noise reduction" actually improve the signal-to-noise ratio or just make the sound more comfortable?

True "noise reduction" algorithms can provide a slight improvement in signal-to-noise ratio (or SNR), and these algorithms are getting better all the time...so newer hearing aids do a better job compared to older technology with noise reduction. Unfortunately, the amount of SNR improvement is not typically enough to provide better speech clarity in noisy situations, except when combined with other features (such as directional microphones). So, the short answer is: noise reduction usually helps to make things more comfortable/tolerable when in noisy situations, but -- when used in conjunction with other digital features -- it can also help contribute to the overall improvement in speech audibility when in noisy situations. 

To answer your question,  in a perfect world. noise reduction should provide a better signal to noise ratio and a more comfortable environment. 

Noise reduction, in most products will lessen what the hearing aid perceives as "noise". When the listening environment has less audible noise, listening to speech is always an easier task. 

Speech understanding in both quiet noise is based upon an individual's ability.  At a minimum,  speech in noise testing and an auditory processing screening should be accomplished to set realistic goals.  

Thanks for asking this question!

Noise Reduction will work to improve Signal to Noise ratio. It will be most effectively noticed if the instruments have been fit and tuned for the person wearing them.  Actual measurement of the hearing instrument performance in the wearer’s ear canal allows for dosing the volume at each pitch correctly.  If some sounds are over amplified and other sounds are under amplified the benefits of signal to noise ratio improvement from a noise reduction circuit can easily be lost. 

Since the noise is getting lower, the signal to noise ratio will increase. It will also make the sound more comfortable.