Microbes need more than sugar to survive, they need elemental nutrients/metal ions as well. Carbohydrates are primarily just sources of energy, due to the chemical energy potential of the C-H bonds.
Some microbes, particularly fungi but also some bacteria/archaea are able to break down complex carbohydrates like chitin, and other complex organic polymers such as lignin. They will utilize simpler sugars if available, but they have to compete for them and bacteria/archaea can multiply much more rapidly. Still, they need to seek out nutrients themselves and they'll have to obtain them from the organic matter around them. Many microbes including fungi excrete enzymes outside of the cell to digest materials and solubilize nutrients, and these can work even without the fungi present.
You shouldn't use too much molasses or products containing simple sugars for other reasons, like the potential for too much microbial activity consuming all of the oxygen in the rhizosphere leading to anaerobic conditions.