As sleepers are only sleepers becuase they have bad dreams, then I suppose they don't have corprus.
After you dispel the Heart, the sleepers seem to get better, but corprus monsters still exist and spread the disease, though it will soon dissipate I would think.
I'm not sure we know that the sleepers do not already have it.
Just as it is said the first sign of madness is hearing voices so the first sign of coprus may be hearing Dagoth Ur. And remember Dagoth Ur offering to mute the Coprus in the Nerevarine? To be persuasive you have to include some truth - and I believe that the strength of spirit (you may add in other attributes) of the carrier of the disease is entirely relevant to the ultimate form the disease takes.
It may then be that Divayth Fyr's 'cure' was more to do with the belief of the Nerevarine in himself, his role in the prophesy and Divayth Fyr's words than the content of that potion? Maybe what Divayth Fyr/the Nerevarine believed to be a cure was in fact a placebo - and the real cure was the force of prophesy which is belief.
That would explain the changes that happened to Vivec, Almalexia, Dagoth Ur and the entire Dunmer people themselves - Therefore, maybe what Azura did was channel that potentiality for change through Dagoth Ur and into the Chimer ... so maybe Azura was the missing link in success that Dagoth Ur achieved accessing the power of the Heart without Kagrenac's tools? And that was how she cursed the Dunmer.
A further detail - look at the nature of change in the Dawn Era ... surely the Heart of a God from that era would be suffused with the potentiality for change ... and when 'corrupted' spirits come into contact with it they show their base or otherwise natures though the outer manifestation thereof. For some if they lack the imagination to fly like the birds of the air or otherwise RAISE THEMSELVES ABOVE THEIR LOWEST NATURES then all they become is base and lowly slugs.