Almost, yes. It will die when state based actions are checked, which happens right after you finish activating the ability/casting the spell you're sacrificing the creatures for if you do so as a cost, or right after the spell/ability that's making you sacrifice those creatures finished resolving if it is an effect.
This sort of ability is a characteristic defining ability, and it updates immediately with the game state changing.
Private Mod Note
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Former Rules Advisor
"Everything's better with pirates." - Lodge (The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science." (Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)