Probably not. Although cellular respiration and photosynthesis are different processes all together, they somewhat rely on each other in the ecosystem (I would say respiration relies more on photosynthesis than vice versa). Without the oxygen produced from photosynthesis, animals (like us) would not be able to undergo cellular respiration. Photosynthesis would still be able to happen without the Carbon Dioxide produced from cellular respiration, as Carbon Dioxide is produced in several means besides cellular respiration.