Tymaret/Butcher of the Horde combo?

[alidayvn]

I have Tymaret, the Murder King, Butcher of the Horde, and a third creature on the battlefield...

If I pay the mana and use Tymaret's ability to sacrifice a creature and deal damage, does that sacrifice also count towards Butcher of the Horde's ability? There's a lot of debate within my circle. The general thought is no, but since you don't need to tap anyone, and Butcher's ability reads almost like an enchantment we're all kind of on the fence now...?