You could stir in a little bark mulch into soil, but little else. A dug hole in clay can create a bowl, crack the edges (and bottom) of your hole.
The addition of a little bark mulch in the hole, and a top dressing of mulch is to give earth worms a home. They will mine water exits your tree will need.
Plan on watering your tree at least weekly, for every week it does not rain. if this is a problem see a watering collar (in addition to mulch)
