I have not done any scientific study related to molasses, but it doesn't take an experiment to know how molasses works and what it does not do; all you have to have is a basic understanding of how soil microbes and plants interact with one another.
If you use molasses, you are not feeding your plant. You are feeding the soil. Microbes utilize the sugar and the additional food causes an increase in soil microbes. As one poster has already pointed out, there is a point of diminishing returns. Plant roots need oxygen, and if you feed the soil microbes too much and allow them to multiply too greatly you run the risk of starving both your plants and the microbes of much needed oxygen.
Additionally, microbes break down the raw material, in this case molasses, and convert it into forms usable by the plants, such as nitrogen, potash and various needed micronutrients. If you are growing completely organically and do not have the necessary micronutrients, nitrogen and potassium in your soil, then the addition of molasses could provide these. If you are using a full spectrum fertilizer, then the addition of molasses is unnecessary as these needed building blocks are already provided.
I think a lot of people become confused about molasses because they think as if the plant is utilizing the molasses the same way we do, and that is untrue. A plant is not sucking up sweet, tasty goodness like a kid with a straw. Adding molasses does not equal a tastier bud. The sugars are not utilized at all by the plant, at least not in their raw carbon form, but instead are utilized when the soil microbes break them down into components the plant uses for its plant functions.
So, is adding molasses a good idea? Well, it could be, depending on how you are growing your plants and if you need the molasses to provide the plant with needed nutrients. As long as it is used in moderation, it should not hurt your plant, and molasses are inexpensive. But if you dump too much, you stand the chance of actually temporarily decreasing the oxygenation in your soil, as well as having an increased chance of either pest or mold, as both insects and mold love the sugars as much as the soil microbes do.
If you are growing hydroponically, molasses does absolutely nothing for you as you do not have the soil microbes necessary to break the molasses down into forms usable by the plants.
In conclusion, molasses are an excellent cheap source of fertilization if you are growing in soil, and will provide some essential nutrients. But if you are already using a full spectrum fertilizer their addition is completely unnecessary, but should not harm anything if you choose to utilize it in moderation. Again, this is not based on any experimentation I have done. It is my opinion based on an educated understanding of how soil microbes and plants work together.