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.
"Customer service was great, and the price was in-line with other places, and fast service. We had a whole replacement of the outside and inside. I would have liked to see a better install for the furnace and new thermostat - the new thermostat should have gone where the old one was, and even tho the new furnace was a tight fit, they didn't offer to come back and repair the case molding, or give me a discount on the damage done, and I believe they should have put a disconnect box on the outside of the home, to make it easier for any future repairs needed. Other than that, am very happy with the cooling and heating!"