Yes it does
Parental Bond allows the Pokémon to attack twice each turn on the same target (even if it fainted), with the second attack being half as strong as the first. This only affects moves that do damage. It does not affect multi-strike moves. Moves that hit multiple targets such as Earthquake and Rock Slide will not hit twice in Double, Triple, or Horde Battles.
Any attack which has a secondary effect has the same secondary effect on the second hit. This includes secondary effects with a chance to trigger and critical hits.