Would have to confirm with @DragonParadox how ritual magic worked while magic was on the low-ebb, but animal sacrifice is like trying to squeeze water from a stone while its in full bloom now. So it would be worse than useless while it's gone.
And I believe ritual magic worked somewhat, but they were things like performing a complex rite for forty minutes to create a spark of mage-light. Sacrifice of inherently magical materials that maintain their enchantments even with low atmospheric ratings of magic in the world (like Valyrian Steel) would produce greater effects according to Brynden, as he gave us the ritual he used in the first Blackfyre Rebellion during Red Grass Field.
Pretty much, animal sacrifice at the nadir of magic is the sort of thing that might give you a flicker of power, enough for practice, but not enough to be useful on its own.