Shambling Horrors do not take conditions with Necromantic Corruption. I noticed I still had many conditions on me even though I had shambling horrors running around and I was specced into Necromantic Corruption. So I tested it out by finding a grub and using Rise to summon shambling horrors. When I was poisoned, the shambling horrors share the poison Dot damage with me but do not actually take the poison from me, I checked both of them to be sure.They don’t take away bleeding or crippled either.