Interesting question.
I was about to say because it's at the end of the damage step... but Grimson's description doesn't say anything like: (Except during the Damage Step like some other cards do).
There's a ruling where if the amount of battle damage you took would make your LP drop below 1000, Grimson's effect cannot be activated. Maybe the same also apply for effect damage?
....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.
That's not entirely true. You only pay for the monsters you're protecting, so against Ultimate Nightmare, you'll only ever pay 1000 if you pay anything.