Is “Faithful Summons” triggered by losing all HP in Wild Shape?

Can you gain the benefits of the “Faithful Summons” feature (Circle of Shepard level 14) if you wildshape into a creature and lose all the creature’s HP?

If you are reduced to 0 hit points or are incapacitated against your will, you can immediately gain the benefits of conjure animals as if it were cast using a 9th-level spell slot.