....Wait, on second thought, it IS the same for effect damage.
Just remembered OCG has a ruling that states you cannot pay cost if it would cause you to lose the duel.
This ruling applies regardless of whether the type of the damage that dropped your LP to below the cost is battle damage or effect damage.
Then yes, you cannot pay because you don't have enough LP.
If you pay 1000, you'd only have 1200 LP left, and you are going to take 2000 damage from Yubel Ultimate Nightmare's effect. So you will lose the duel because you pay a cost. To prevent this, game mechanic rules that you are not allowed you to pay.