Zoro whilst attempting to tame Enma said: "Give it back to me" obviously referring to his general energy and also haki after his arm had shrunk in size. However I believe it's extensively unlikely that Enma is capable to permanently store these even if the user wished to, and eventually the energy would be converted to another form, and regardless Oden's arms were normal before he died.
Kaido talks about presence, not even haki, and swords are living objects canonically, eventually Enma simply stored his memories, but that has to be proven later on.
Also I believe that the black blade is decidedly not about storing haki in the sword, but eventually render it particularly hard without storing it, since Zoro failed to cut up Monet.
