Not quite.
Spoiler…
The tea Perez was giving the emperor was also a poison, one that kills oh so slowly. His revenge is sweet as fvck. He wouldn’t let that dumbass emperor die that easily.
Oooh... Shucks
That is a hilarious plotcucking of the Empress and makes me happy. Because it's obvious to everyone with half a brain that, when cornered, the Empress would just kill the emperor and seize the throne because she can. So I would be enraged if such an obvious thing brought all our MCs scheming to a crisis. That is how a mediocre series would generate drama. Thankfully this seems to not go that route.
My theory... The emperor won't die.
Because of the tea Perez gave him.
WHAT IF that tea was an antidote??? The poison will shake him, but not kill him.