Yes they will definitely try that (let's see how much they succeed this time around). However the OP was talking about a pandemic treaty, so it would have to be a pandemic to apply
Discussion
No, they can declare pretty much anything as a health emergency, climate being one and there’s zero comeback
We have a large group of doctors who are lobbying to make climate change a health emergency. They have been at all of the big health and climate change events. It seems like this is the way the narrative is heading.