Whether LC & MJH ever played together during the Great Folk Scare, I don't know. I think it's unlikely that they would have prior to that - Cotten was a domestic in the Seeger household in the '40s and before, I believe in Washington DC - Hurt was a tenant farmer in Mississippi. But you're on the right trail with "pre-existing music" that would have influenced both, perhaps. But I suspect the tree to be barking up has Eubie Blake and Scott Joplin in its upper branches. One of the defining characteristics of both Cotten & Hurt's style is the thumping, contrapuntal thumb that IMO comes straight from Ragtime. And the chronology is perfect - ragtime was at its height when both were "coming of age."