Well, the first time I saw this clearly demonstrated was in my game as Mictlan, where my Luck scale had won me a Soul Contract, but the carrier of it was unexpectedly ambushed in the field and killed by C'tis, who brought with them a bit of miasma. A Mictlan Priest found the contract, but caught disease, and I proceeded to hide him in my capitol with a ring of regeneration. Fairly often he would get a new affliction, but he had low base hit points, so I interpreted it as a logical consequence of the damage, rather than a direct effect of the disease. If you've seen many afflictions on diseased high-hit-point units, then that would suggest it was more like a flat chance from disease.
Whether it would increase the chance of afflictions from battle damage to have a disease, I don't know, but I don't expect so, just reflecting on what I've seen.
As has been mentioned (but to clarify, since it is the thread topic), diseased undead still don't suffer new afflictions merely from the disease.
(BTW, details of my Mictlan Priest were given on
the Affliction Record thread .)