I am not sure I am following 
So my scene has standard type material, lit, no real-time lights (yet), baked lightmaps. Some of the materials will have emissive texture plugged into it emissive socket (think glowing eyes; but at this moment I don’t have any).
The issue is that when I bake lighting (skylight in particular), I get no difference in lighting at all. As if material is full bright. I removed all lights except tiny point lights I had as decorations, baked lighting - nothing. The level is all well lit. I added bright direct light, baked lighting - got shadows and some variations in how level is lit. Shadows however remained as they were when I had no lights in the scene. So then I disconnected fogging material function from emissive socket and bam! lighting looks right now, but of course I get no fog 
Kinda catch 22.
Here is the current, fogget setup that makes fog looks really good, but interferes with the lighting
This is your fogging function, with Power node added to make fog look like what I want:
level geometry material with fogging function from above:
