Only at the 99.9% level, and only briefly before the majority of the remainder look at the open and empty planet and go "oo, nice, free land for a big family".

If you "solve" this in any way other than giving people better options for them that are inherently also better for the environment, it's unstable — even if almost every nation tries to enforce it at the same time, whoever defects (in the Nash game theory sense) literally inherits the Earth.

(And that's why I'm also expecting Von Neumann machines to be the environmental disaster of the solar system within a century of someone making one: game theory says that whoever does that sucessfully, inherits the future light cone).