Yes, plants can do photosynthesis and cellular respiration at the same time. When sunlight is available for the plant, the plant can use that energy to perform photosynthesis. The major product of photosynthesis is G3P, a 3 carbon molecule that the plant can use to make glucose (it's own food), or other substances like proteins or lipids that it needs for other life processes. Let's stick with the glucose for this example, though.
As mentioned, a plant produces glucose as food for itself. In order to use this food for energy, the plant must perform cellular respiration. Just like in animals, glucose is broken down during cellular respiration in plants to produce energy in the form of ATP. This is chemical energy that the plant can use during chemical reactions in cells that require energy.
So, not only do plants perform both photosynthesis and cellular respiration, but as long as there is sunlight they can perform both at the same time.