archlord krystia ruling

If you have exactly 4 Fairy-Type monsters in your Graveyard, you can Special Summon this card from your hand. When you do, add 1 Fairy-Type monster from your Graveyard to your hand. Neither player can Special Summon monsters. If this face-up card would be sent from the field to the Graveyard, it returns to the top of the owner's Deck, instead.

The part on "When you do, add 1 Fairy-Type monster from your Graveyard to your hand", does this effect works only when its special summoned by the condition of having exactly 4 fairy-type monsters in graveyard?
so if i special summon by valhalla, can i still add i fairy-type monster from graveyard to hand?

Must special summon that way then can add back.