No.
The second sentence of Yawgmoth's Will creates a replacement effect. The Shadowborn Apostles aren't exiled from the graveyard; They are never put there in the first place. No matter when you activate (not trigger) No Rest for the Wicked's ability, it can't bring them back.
During the activation of Shadowborn Apostle, the Apostles are sacrificed and exiled. They go to exile instead of dying. Yawgmoth's Will moves those cards to exile "instead" of being "put into your graveyard".
No Rest for the Wicked, no matter when you resolve its ability - in the full range of states passed through by the game, including times that you can't resolve an ability of an enchantment - will never raise those Apostles because they are never in your graveyard.
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The second sentence of Yawgmoth's Will creates a replacement effect. The Shadowborn Apostles aren't exiled from the graveyard; They are never put there in the first place. No matter when you activate (not trigger) No Rest for the Wicked's ability, it can't bring them back.
No Rest for the Wicked, no matter when you resolve its ability - in the full range of states passed through by the game, including times that you can't resolve an ability of an enchantment - will never raise those Apostles because they are never in your graveyard.
Awesome avatar provided by Krashbot @ [Epic Graphics].