Ruling Question about Agatha’s Soul Cauldron and Activated Ability’s Cost | tcgmode

Say I use Agatha’s Soul Cauldron and exile a Doomed Necromancer to copy his ability to a Shadowborn Apostle with a +1/+1 Counter on it. Since the cost to use Doomed Necromancer is one black mana, tap and Sacrifice “Doomed Necromancer”, can Shadowborn even use Doomed Necromancer’s ability, since ...