If no one in your household suffers from allergies or unexplained symptoms or illnesses and if, after a visual inspection of the inside of the ducts, you see no indication that your air ducts are contaminated with large deposits of dust or mold (no musty odor or visible mold growth), having your air ducts cleaned is probably unnecessary. It is normal for the return registers to get dusty as dust-laden air is pulled through the grate. This does not indicate that your air ducts are contaminated with heavy deposits of dust or debris; the registers can be easily vacuumed or removed and cleaned.
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.
All these pro duct cleaners answer with "it's common sense, everything operates better when cleaner" etc. But your explanation is correct. Especially so with flex tube ducting where dust gets "stuck" between the lowest valleys (between wire coil supports) where air flow is drastically reduced -- which is more than 50 pct of the entire interior surface area of the flex ducting. That sounds like a bad thing but also has a good effect of trapping dust from escaping.
You may consider having your air ducts cleaned simply because it seems logical that air ducts will get dirty over time and should be occasionally cleaned. Provided that the cleaning is done properly, no evidence suggests that such cleaning would be detrimental. EPA does not recommend that the air ducts be cleaned routinely, but only as needed. 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.