No, it has an Ability, it just has no effect once it turns into Complete Form. Similarly to Mimikyu's Disguise or Zoroark's Illusion — once it has been broken, it has cannot be used for the rest of the battle. Once 10%/50% Zygarde reaches half health, the ability activates.
So to answer your question, Zygarde Complete does have an Ability, it just doesn't do anything.
