Add fake displacement from shaders to true displacement for an accurate displacement baking


I am currently building a terrain scene and baking material displacement (the one going to the material output node) but there is a problem : This baking is missing fake displacements (normal) from the shaders going trough the suface input of the material output node. My bake type is “Emit”.

Is this possible to bake the full displacement (true displacement + fake displacement) ? I have tried many nodes configuration to add the fake displacement to the true displacement without any success.
Maybe I don’t have the good workflow ? Maybe I don’t have to use fake displacement on shaders, but get the shaders “covering area footprints” then apply to these areas a true displacement specific to each shaders?

I am baking the displacement from the procedural shader to generate a heigtmap converted to a solid used as an underlayer base (very little inside Z offset ) to the same procedural shader. That way I am able to get a solid interaction with the underlayer (for example to add particules) , but keeping a good looking procedural surface.

Thank you in advance for your replies!