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.
If you don't agree with duct cleaning, fine. If there are some things that HVAC people can do to make the system need cleaning less often fine, but to suggest that I need to GO TO JAIL????? If you need to knock others to make yourself look better....... If duct cleaning is such a scam, why are their governing bodies like NADCA (which I do NOT belong to),several manufacturers of equipment, and national restoration franchises (I'm not a franchise either) who provide this service? I guess the whole world is stupid and only HVAC people are smart. I suppose I am scamming them when I clean puff backs, water damage, fire damage, and clean their carpets too? Or did I wake up one morning and say "ya know, it is great to be a hard working, honest owner operator, but I would love to provide a service that unlike everything else I do is a con and rips off the 90% referral business I busted my butt to earn"
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?).