In short, is there a relation between the preposition cum and the conjunction cum?
It makes some sense that the conjunction would come from the preposition. One could interpret some cum clauses so that the main clause happens with a condition expressed in a subordinate clause or at the same time with the subordinate clause. Perhaps some other kinds of connections would make sense, too.
I have seen both cums discussed in many places, but I have never seen any comparison between them. Is the similarity a coincidence or not?