No if you give your Muk a Toxic Orb to hold it will do nothing at all for Muk. A Toxic Orb inflicts a Pokémon with the badly poisoned status condition after one turn of battle.
Inflicts the holder with bad poison after one turn of battle.
That's all the Toxic Orb does nothing more nothing less. However if a Pokémon such as Gliscor with the Ability Poison Heal is given a Toxic Orb to hold, Gliscor will restore 1/8 of it's maximum HP at the end of every round, once the Toxic Orb has activated, and Gliscor has gained the badly poisoned status condition. If the Toxic Orb is removed via Knock Off or Trick etc., or Gliscor is infected with another status condition prior to the Toxic Orb activating, the Toxic Orb will not infect you with the badly poisoned status condition, and therefore you will not gain 1/8 of your maximum HP back at the end of every turn.
Okay the relevant information:
Muk does not have Poison Heal as one of it's Abilities, and even if it did it wouldn't work in restoring it's HP back. As Muk is immune to being poisoned and badly poisoned since it is a Poison type, so if you did give your Muk a Toxic Orb to hold it wouldn't do anything at all, since Muk can't get badly poisoned.
However there are two items, one of which you can give to Muk to hold to restore it's HP back each turn, these items are Leftovers and Black Sludge. Since Muk is a Poison type Black Sludge will restore Muk's HP by 1/16 each round. If Muk wasn't a Poison type Black Sludge would damage Muk by 1/8 each round but since Muk is a Poison type your okay to have it hold it. Leftovers will also restore Muk's HP by 1/8 each round so it doesn't really matter which you give Muk to hold as they restore the same amount of HP.
Source: Knowledge and Experience
Hope I helped :)