Plants roots cannot really absorb sugar. Plants can make their own sugar via photosynthesis. They can do this so efficiently that they have enough to spare; releasing it and other substances into the rhizosphere (root zone), in order to attract, stimulate and to some extent control microbial populations near the roots.
In soil and even in hydroponics there is competition for carbohydrates (including simple sugars) among microbes, which are endemic to soil and may be introduce to hydroponics via many products. In particular, bacteria are best able to utilize simple sugars (glucose, fructose, sucrose) as they are able to multiple rapidly.
Blackstrap molasses contains the least amount of sugar among the different grades of molasses. It is the final by-product of sucrose refining, or 3rd molasses, based upon the number of times the cane or beet juice was boiled to extract the sugars. It has a significantly higher concentration of minerals, including potassium (K), Ca, Mg, Iron and other trace elements. It also has cyclic hydroxamic acids which chelate or complex with minerals such as Iron, increasing their availability to the plant.
Don't use more than a couple tablespoons per gallon in soil and I would imagine pushing it isn't a good idea for hydro either. Usual usage for soil is from 1 tsp to a tablespoon per gallon. Do not let molasses mixed in water sit around. Mix it and use it immediately if you aren't going to aerate the solution.