In some cases you can. Especially if your air conditioner is under heavy load, having your cleaning crew periodically dust the coils and remove debris around the unit is a great idea. Make sure they don’t use water around the electrical components!
However, you still need to have your coils cleaned and your system tuned up at least twice a year by a professional. We use special chemical cleaners to remove scale and buildup, and we clean parts that are dangerous for untrained maintenance staff to handle, such as the fan blade. We keep drain lines clear and empty drip pans to prevent mold growth. Certified HVAC techs check electrical connections, refrigerant charge, and also inspect the entire system for worn parts and any signs of impending trouble. You don’t want your cleaning staff handling these tasks.