The short answer is yes, sugar does help plants grow. However, excessive amounts of sucrose can be harmful to a plant. For plants growing hydroponically or in a selective medium such as in a petri dish, sucrose is often used as a carbon source for sprouting plants. Plants make sugars through photosynthesis by combining water and carbon dioxide. Plants use carbon dioxide as their main carbon source so they do not need sugar in their substrate to grow. But young plants and tissue plant clones that aren't yet efficiently producing sugars through photosynthesis can benefit from the extra carbon stored in sucrose.
Sugar water used in a plant's natural environment can also attract other organisms and bacteria. Although some may be symbiotic (help the plant), many can interfere with the plant's growth or even cause it to die.