Do plants need O₂ to consume energy they've stored via sugar?
Plants need sugar not only for energy but also for synthesizing essential metabolites and building blocks including cellulose (used in cell wall), glycoproteins and 5-carbon sugars for nucleotides. 

As already mentioned by canadianer, plants respire by oxidizing sugars. This happens mostly during the night. However photosynthesis also produces ATP and therefore plants are not strictly dependent on respiration for energy. Moreover the fixed carbon in the form of starch makes up an energy reserve (like fats and glycogen in animals).