Yes and no. It'll work outside of the damage step, but if you're thinking of using this after your monster is destroyed by Golem, then it won't work due to Golem's effect.
Can't use Michizure if Ancient Gear Golem (or another Ancient Gear with similar effect) destroys a monster, but you can still use Michizure on Ancient Gear Golem if for example Vorse Raider or Tribute to the Doomed destroys your monster.