Yes the duke ends up drinking it because it is revealed
that he was the one who gift it to the empress. He did it for the empress' best interests. How cute of him ><
He drinks it to prove to the empress its effects (and because he has an antidote so he's not worried), then falls in love with the empress under the effects of the potion. He says such sweet things to the empress afterwards, making the empress wonder is this how it feels to be loved.. Poor Navier T T