Yes, plants need and use oxygen to process glucose.
Not every plant cell has access to sunlight energy in order to perform photosynthesis. In order to make energy in those cells, the plant must burn sugar. This process is called cellular respiration, and it is the same process that humans do in order to make ATP energy. The process occurs in the mitochondria of a cell, and plants do indeed have mitochondria in their cells. Cellular respiration has a lot of steps within it, but the basic formula is the following:
sugar + oxygen --> carbon dioxide + water + energy
That formula is basically the reverse formula from photosynthesis. The photosynthesis formula is the following:
carbon dioxide + water + sunlight --> sugar + oxygen
As you can see, the products of photosynthesis are the raw materials needed for cellular respiration. Plants don't eat in order to consume glucose, because the plant produces it. The plant then takes the sugar that it produces and burns it during cellular respiration, and the plant needs oxygen to make that reaction take place.