Over time, even sharp angles in an HVAC duct can become worn and degraded from the constant friction of passing air. Indoor wiring and conduit is not insulated or intended to be subject to the sort of fluctuating temperatures found in an HVAC duct system. The temperature changes, coupled with constant friction from passing air, can degrade the insulation on the wires and eventually lead to short circuits.
An especially dangerous scenario involving wires in an HVAC duct is an electrical fire. The fumes from burning insulation and metal wire will be quickly and efficiently spread throughout your home by way of the HVAC system. This can be a potentially dangerous situation because people inside the home can be overtaken by fumes before they have any idea a fire has broken out.
Running wires through an HVAC duct may seem like a great idea while you have the duct off, but imagine having to pull out the ductwork to conduct repairs. Needing to shut down your entire HVAC system to repair or replace a frayed or faulty wire inside one of your ducts would be an unwelcome task in the heat of summer. Spend a little extra time now and run your wiring in a conduit separate from the HVAC ducts.
Running wiring through an HVAC duct likely constitutes a void on your homeowner's insurance. Insurance companies take improper wiring very seriously and, if it is proven that a fire or other damage was caused by improper wiring, you will not receive compensation for your losses. Check with your insurance company and local code enforcement agency to ensure your proposed wiring schema is up to code.