I do not think a cultist, no matter how bad, can tank relationships, the Empire is quick to disavow those and the Dawi are not unaware of their existence, heck, they have their own even if its much rarer and causes them much shame each time.
He could, however, cause a honour chain raction of slayers and make the Dawi somewhat more suspicious and untrusting of either umgi as a whole, or mages.
Edit: and no, Malekith doesn't count, because unlike the Empire, the elgi didn't disavow him. After 2 diplomatic overeaches. Where the Empire would be the one sending the diplomats if a wizard turned cultist. My point admitedly assumes that whoever is in charge of empire diplomacy is either smarter or humbler than Caledor 2 (not a big hurdle, but still, Dieter IV was real), but at that point, a cultist is not the main reason for the tanking of the relationships, just the igniting spark.