Carbs are most of what's in compost besides living microbes, as well as the balance of the material in meals after you subtract out protein. Yes, you hit the nail right on the head, lep. As long as the chain of microbial metabolism in the soil can keep on a churnin', all of the above will keep on a burnin'. Fertilizer just grows grass. Compost &/or meals build the quality of soil that supports the grass.