Will Zoroark with Black Sludge work?

Question

I have a Zoroark in the front of my team and a Muk in the back of my team. If I give my Zoroark the item Black Sludge, will the "Muk" that I send out at the start of the battle gain HP from it?

Answer 1

No.

Zoroark only copies a Pokemon's appearance, not its moves/ types. It will remain a dark type until hit, so it will take damage from Black Sludge.

Answer 2

No, it won't. Black Sludge only heals damage for Poison types. And Zoroark's Illusion is exactly as it sounds; a mere illusion. Behind that fake appearance, it's still a Dark type, so it will still take damage from Black Sludge.
As a friendly note, it would also give away Zoroark's disguise, which is the last thing you want.

Hope I helped!