The beginnings of this functionality already exists /src/AMEE-in-Revit.Addin/Commands/AddCO2eParameterCommand.cs, but for some reason it doesn't work.
So, for now you need to manually add the CO2e Parameter to all elements
View > Schedules > Material Takeoff schedule > Multicategory > Add parameter > Shared Parameter > Select CO2e parameter > Add to all elements in selected categories > check Instance > check All > OK