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.
As a person with severe mold allergies, I live in a the South where the climate naturally breeds molds.We noticed a difference when we had our ducts cleaned.The company used a vacumn type system and covered all of our vents with plastic that was held up by the suction. We had no damage, no leaking dust/dirt back into the house and it took several hours. I think if you use a reputable company it makes the world of difference. Now we use better air filters and also have a UV light to prevent mold growth on ours system.We 'd do it again when the time comes. From your car's air filter to your dryer...anything works more efficiently when it is not filthy dirty.That's just common sense.
EPA does not recommend that air ducts be cleaned except on an as-needed basis because of the continuing uncertainty about the benefits of duct cleaning under most circumstances. EPA does, however, recommend that if you have a fuel burning furnace, stove, or fireplace, they be inspected for proper functioning and serviced before each heating season to protect against carbon monoxide poisoning. Some research also suggests that cleaning dirty cooling coils, fans and heat exchangers can improve the efficiency of heating and cooling systems. However, little evidence exists to indicate that simply cleaning the duct system will increase your system's efficiency.
If you are replacing your air conditioning system, make sure that the unit is the proper size for your needs and that all ducts are sealed at the joints. A unit that is too big will cycle on and off frequently, resulting in poor moisture removal, particularly in areas with high humidity. Also make sure that your new system is designed to manage condensation effectively.
Air duct cleaning service providers may tell you that they need to apply chemical biocide to the inside of your ducts as a means to kill bacteria (germs) and fungi (mold) and prevent future biological growth. They may also propose the application of a "sealant" to prevent dust and dirt particles from being released into the air or to seal air leaks. You should fully understand the pros and cons of permitting application of chemical biocides or sealants. While the targeted use of chemical biocides and sealants may be appropriate under specific circumstances, research has not demonstrated their effectiveness in duct cleaning or their potential adverse health effects. No chemical biocides are currently registered by EPA for use in internally-insulated air duct systems (see Should chemical biocides be applied to the inside of air ducts?).