Kaido talked about Oden's presence to be accurate, not haki. The terminology is debatable after establishing this notion.
So I substantially doubt he referred to a living spirit, that would be extensively strange.
Maybe since swords are living objects they can store memories, but haki from people indefinitely?
I don't think so. Most likely not, also for a logical matter... why would Oda likely portray a sword capable to turn nigh invincible by storing haki from countless users and still be tamable.