Yes. Damage is “added” simultaneously to Mugglug and the Mud Drudger. (See Simultaneous Effects, Exceptions, FAQ p.15). When the damage “would be” added to Mugglug, Prune triggers and changes that effect into destroying the Drudger–before the damage on the Drudger destroys it. This also means the user of Volcanic Blast or Mortar gains no magic from the Drudger, as the Drudger is destroyed by Prune and not by the damage.