If I use Beedrill's "Allergic Shock" attack, and then on the following turn I use an attack that does damage and the Defending Pokemon is KO'd, can the opponent add extra damage if they use an attack like "Revenge" or "Retaliate"?

If damage from your attack on the following turn is enough to KO the Pokemon, then the opponent would get to add extra damage for Revenge/Retaliate because their Pokemon was KO'd due to damage. But if there wasn't enough damage to KO the Pokemon and it gets KO'd due to the effect of Allergic Shock, then the opponent would NOT get to add extra damage for Revenge/Retaliate.

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