In general Knygatin, the answer to your question is no. I've read a fair amount of CAS' extant correspondence, and as a rule, his letters tend more to the "meat and potatoes" apsects of the creative process, and less towards "deeply personal revelations" and how they might impact that process. Of course, there are some exceptions, since CAS often does comment on poets that he admired (Charles Baudelaire, Ernest Dowson, Edgar Allan Poe, etc), but his analysis as included in the letters is usually quite brief.
It seems to me that in many ways CAS was a fairly reserved person, even in his letters with correspondents that he communicated with over many years.
As a specific example, one of the letters in
Born under Saturn briefly discusses the source of his poem "Witch Dance", but only in very succinct terms. I included the relevant quote in a blog post for anyone that might be interested:
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www.desertdweller.net]