If Karthus dies, does Battle Trance still apply/scale up?

Since dying is a major part of his kit, does the effect still apply? I assume it does since he is in somewhat of a dead/not dead situation when he is "killed". Also just for clarity sake, does the scaling apply only if the champion (the actual character) is in combat or anytime when they deal damage? SO like if Teemo's shrooms gets triggered and he is no where near it (say he backed and something in lane triggered one), does that start the scaling?