This is generally not a good idea. First, when cooling, when the compressor shuts off in single speed systems, you will re-evaporate lots of water back into the air. Second, even new duct systems can leak a lot, up to 5% is a pretty good figure, I think. The more you run the fan, the more air you lose. Not only do you have that percentage losses, but induce pressure differentials from room to room and from outdoors to indoors. If you have outdoor ducts (That includes attic and crawl spaces, outside the envelope, basically.) you get inside-outside differentials. Return leaks pressurize the house which is somewhat better than leaks in the supplies which depressurize. It depends on where the return is sucking the air from. If it is a damp crawl, not so good. If you depressurize the house, you are sucking air in through any small gap anywhere. If it is hot and humid, you can have immediate condensation there and mold grows. Leaks turn the AHU into a power vent with uncontrolled intake or exhaust points. Leaving the fan on constant circulate makes it into a much more effective power vent.Leaving the HVAC in circulate mode is an option. Any fan running will introduce heat into the structure... something to keep in mind regardless.
Inside-outside pressure differentials are not going to happen if your system is entirely within the envelope where it should be, but you can still get room to room differentials that can pressurize and depressurize individual rooms.
Duct leaks cause dry indoor air in the winter.