There are several things to look at here.
1) If you have a temperature balance problem in your house, running the blower 24/7 will help even that out because you will be circulating air when the compressor is off.
2) Running the blower geves you a breeze throughout the house, kind of like having a ceiling fan in every room. This will make you feel cooler at any given temperature. However, it will use more electricity than ceiling fans, because it has to push air through the resistance of a duct system.
3) The motor in a furnace is designed to run continuously. You will not hurt it that way. With that use, oil it once per year with 20 or
30 grade non detergent motor oil. Do NOT use WD-40 or penetrating or
3-in-1 oil. Do not oil it too often. more oil will overflow the bearings and gum up the motor by catching dirt and holding it.
4) Running the fan that way will allow your filters to catch more dirt, keeping dust levels down.
5) NOW THE BAD PART! When the compressor is off, you will re-evaporate the water left on the coil and in the drain pan, raising the relative humidity in the house 10 to 15 percent. I have tested this using data loggers to record humidity levels in my own house. Lennox has done studies and determined that as well. If you are in a high humidity area, The extra humidity can make you uncomfortable and allow mold growth.
6) If you run the fan this way in the winter, the house will feel drafty.
ONE OTHER THING! DO NOT close off the registers in rooms that you are not using. That restricts air flow and can damage the compressor if it is running. Freon flow is what cools the compressor motor, and Freon flow in part is controlled by air flow. Also if air flow dirops too low, you can get liquid Freon back to the compressor, which is very bad for the compressor. The biggest enemy for the furnace fan motor is heat and restricting air flow reduces the amount of heat removed from the motor. At least that is what the A.O Smith motor rep tells me.
So running the furnace fan is a mixed blessing. Whether it is right for you depends on your climate, electric rate and your situation.
I hope this helps.
Stretch