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.
The key to the continued and efficient operation of your heating and cooling system is periodic maintenance. Cleaning the air duct vent system, and servicing you heating and cooling equipment will keep the system operating at its peak performance. Air ducts are cleaned for two reasons. One: to prevent debris from entering furnace and air conditioning components. Two: to prevent debris from cycling through the home. The air duct cleaning contractor needs to employ cleaning methods which successfully removes debris, and ensures that debris does not enter the occupied space. Most contractors can verify the results of the cleaning through video or pictures.
Hi guys if your not convinced yet that duct cleaning is a waste of time. I’m a HVAC business owner install heaters and air conditioners. Simple facts if you have an old system get a new return air fitted with a filter it will catch all the dirt and dust. If you still have as many do black flecks and stuff coming through it is the lining inside your ducting that has perished. So somewhere you have a hole or very old ducting. If you had rats etc its a hole somewhere. To clean, stick your vacuum in the outlet and push the hose as far as it will go this gets 99% of toys and coins fur and alike. Think about it if the object is not heavy it will come out the duct when unit is on. Service the heaters or air con units but not the ducting. I would go further to say that duct cleaning actually damages the ducting in my opinion.
The key to the continued and efficient operation of your heating and cooling system is periodic maintenance. Cleaning the air duct vent system, and servicing you heating and cooling equipment will keep the system operating at its peak performance. Air ducts are cleaned for two reasons. One: to prevent debris from entering furnace and air conditioning components. Two: to prevent debris from cycling through the home. The air duct cleaning contractor needs to employ cleaning methods which successfully removes debris, and ensures that debris does not enter the occupied space. Most contractors can verify the results of the cleaning through video or pictures.
When you hire someone to put up wallpaper or build a fence, it's easy to see whether it's a good job. But with services like air duct cleaning, there's much more risk of fraud because the homeowner can't easily check the work. A disreputable company may not have the proper equipment to do a quality air duct cleaning job, may overcharge you, may leave the ducts dirty or filled with debris and may even do costly damage to your home's HVAC system. Some companies entice you with very low offers, such as $59 for a whole-house cleaning, then pile on extra charges. 
Most people are now aware that indoor air pollution is an issue of growing concern and increased visibility. Many companies are marketing products and services intended to improve the quality of your indoor air. You have probably seen an advertisement, received a coupon in the mail, or been approached directly by a company offering to clean your air ducts as a means of improving your home's indoor air quality. These services typically — but not always — range in cost from $450 to $1,000 per heating and cooling system, depending on:
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