How does noise reduction for speech recognition differ from noise reduction that is supposed to make speech more "intelligible" for humans?
I don't really find papers that discuss this difference.


There are whole books on the subject:

Robust Automatic Speech Recognition 1st Edition


  Do speech intelligibility and speech quality correlate with the accuracy of speech recognition systems? 


Usually no, usually noise reduction corrupts features in unpredictable way and reduces speech recognition accuracy.


  Are there objective measures that can evaluate how "good" a denoised speech signal will be for a speech recognition system, for example if also given the original clean speech? Or is the only way to find out how good your noise reduction technique is, to train the speech recognition system on the denoised data and look at the accuracy?


Second. Moreover feature-based noise reduction actually removes important information from the spectrum altogether so you can not repair an accuracy of the clean system. For that reason modern approach is to perform multi-style training on noisy data instead of using noise reduction algorithm beforehand. It ends in more accurate recognition.