The short answer is yes, duct cleaning, done right by a reputable company will help with the smell. It is likely though the smell is coming from another source, ie the crawl space. It could also be that another rodent is dead in the duct work. A visual inspection would be in order to check for any breach in the duct system. A duct pressure test would be able to tell you how much air is leaking from the system over all. A hole large enough for an animal to enter would loses a great deal of air, over 300 CFM. It would be worth looking into having this test done and it should cost around $200. Cleaning the air handler and evaporator coil will greatly improve the performance of the air conditioner. Dirt and dust on the evaporator acts as insulation and reduces the amount of cooling done be the coil. Any quality duct cleaning should include cleaning the air handler and coil, and the tech should allow you to watch him perform the work as it is done.
You and your family spend hours sitting on your favorite chairs, couches and sectionals. Over time, dander and body oil become trapped in the upholstery, but with regular cleanings you can keep these delicate fabrics looking, feeling and smelling great. We examine your furniture and select the best process to safely clean and protect any kind of upholstery, including leather.
Some research suggests that cleaning heating and cooling system components (e.g., cooling coils, fans and heat exchangers) may improve the efficiency of your system, resulting in a longer operating life, as well as some energy and maintenance cost savings. However, little evidence exists that cleaning only the ducts will improve the efficiency of the system.