Have EEG signals in auditory speech perception task have ever been analyzed for correlation with auditory stimuli itself? This can be useful for getting a better grip on understanding the link between actual stimuli, brain processing, and EEG data.
Extensively. Most prominently, recently, by David Poeppel, Oded Ghitza and Anne-Lise Giraud, in a series of papers. They've, to be precise, mostly focused on MEG  correlations with the filtered speech amplitude envelope. Areas around the auditory cortex track it fairly well it seems. There is still much debate about what this means and where it comes from, but it's been discussed. Example here.

There is also the spectrotemporal response function, which is a somewhat generalized concept and mostly employed in an sEEG context. Example here. It looks like this: