Sure looks like its sucking Haki up to me. This is the way it works to me: a well-made sword can inherit the spirit of its wielder if they're strong. Enma, however, is a special case, as it literally absorbs then unleashes Haki. This is what makes it a powerful blade, but dangerous. You have to regulate your Haki flow, and let the blade absorb Haki, rather than let it suck all of it out of you at once.
Think of Zoro's Haki like a finger pinching a straw to keep Enma from sucking up his Haki, then releasing it as necessary.
When Zoro used Flying Dragon Blaze, he was unleashing the Haki he had stored in the blade.
Since Enma sucked Oden so much (wut), the blade is full of his Will.
Zoro was willing to bow down to Mihawk. He already took Ryuma's sword, why wouldn't he used Oden's?
I'm not saying Zoro can use Oden's Haki, I'm saying Oden's Haki changed Enma. The sword literally thirsts for the blood of Kaido. If Enma isn't used to kill Kaido the entire arc with this sword was a stupid waste of time.
Uh, I also think it's possible to hear a prior user's Will in their sword/fruit through the Voice of All Things. We'll get some Force Ghost stuff with Joy Boy at some point