Does baking a scene lighting also apply the Volume (Post- processing)

I need to change the skybox when a level is loaded and at the same time I will instantiate the appropriate Post-Processing Effect (Global Volume) for that Skybox and here’s the thing I need to bake the lighting of each scene to improve performance.

My question is:

If I Bake the lighting for a scene without the Post-Processing then Load this last one
(the Post-Processing) at runtime will this make backing the light useless?

Or does loading the Post-Pocessing at runtime have some draw back that I need to be aware of ?