If someone kills you when you're ulting as Karthus, does your ult go on cooldown or does the channel continue while you turn into a zombie?
Following the general rule of channeled spells, if a channel is interrupted in any way, the ability goes on cooldown. If the caster is killed, the channel is interrupted.
Skip everything below if you are against "fun":
I once dropped a karthus to 1/10th of a bar, and he thought that he was dead. I had very little HP, so he decided to cast Requiem. I went up to him and bashed him in the face, thus killing him. Channel interrupted, Karthus pissed off, Ult wasted, Team saved: Mission accomplished.
Also, Karthus is a skeleton, thus allready undead, and can not turn into a zombie. What happens is that karthus becomes ethereal, or as you "Humans" like to name it - a "Ghost".