Feeding the Pit

ASK FANTASY FLIGHT 

Q: If Feeding the Pit is undamaged, can I still use the action on it to discard a captured card? In addition, will I still be able to draw a card?

A: Yes you can discard the captured card. That is the cost to be paid. But as there is no damage on the objective, nothing is healed. Since nothing is healed, the "then" effect following it does not resolve either.