No, he didn't. He saw the Dai Li take Jet away, but that's it.

So no hugs from Azula?

Or what's broken to their advantage? No, that would be... inconvenient.

Zuko would spend most of his time running after Kuei going "NO! Bad idea, don't do that, put that down!" Makes him feel very wise and knowledgeable. And incredibly sympathetic towards his uncle. Kuei could use a little over-dramatic anxious Zuko dose.