Depends on what you want for your grunge. I would use layermapping to create and apply the grunge material to the surface of your object. I would also create a bump map using a grayscale version of the same layermap.
Assigning a layer (or precomp) to a layer is part of the process.
Now you need to be sure the material you're applying to the object includes the layermap. You'll want to either edit a material or create a new one and use the layermap popup to choose the layermap number you've assigned.
Then apply the material to the object, if you haven't done so already. Does this help?
I think I get what you're asking - why not use a precomp as a layermap that includes your black and white grunge map applied over a solid color or whatever else you're using. Using layermaps gives you the freedom to create incredibly complex animated materials to apply to your objects.