Allergies, emphysema, asthma and other health concerns are tied into the air quality of your home environment. Dust mites and sporiferous allergen thrive in damp environments. A good dehumidifier linked into the central duct system under the plenum will condense air moisture and drain off the moisture through a drain tube when the central air system is on. Central cooling also helps to create dryer air, but a dehumidifier that can remove so many pints of water per hour is much better.
Use in conjunction with an air exchanger means that fresh air is pulled in from outside (instead of recycling internal air) and ambient (internal) air is then removed from the home. This means that the air exchanger - exhanges old air for fresh from outside and the dehumidifier removes much of the moisture before as it enters the home. The health benefits would certainly outweigh the initial and operating cost of the exchange system, especially for children or the elderly with who often suffer from chronic respiratory illness, exasberated by indoor pollution.
Most importantly, keep in mind that annual maintenance must be performed to clean dust trapped in the condensor coils in both the dehumidifier and the A-coil of the air cooling system in the plenum. Otherwise the objective behind installing this system would be somewhat compromised.