I have central air in my business which is 1 story. I have been told to leave the heat/air funace fan on during cooling. Does this help keep it cooler?

Nope, it does not dehumidify as well and will NOT cool the air at all, because it is just recycling the room temperature air. It's like setting up a desk fan or ceiling fan, it just blows room temp air around (not cooling it).

But isn't it true that the fan still moves air across the A-coil which is cooler, even though the condenser is not running?

That may be true, but by the time the air reaches the exit vent, it is room temp. When the compressor is on, air coming out of the handler is about 35 degrees, but by the time it reaches the exit, it is about 20 degrees higher.

I leave the fan on for circulation.

There is a thing called "The Wind Chill Factor". In the winter and the temp is 30 degrees and the air is blowing at 5 miles per hour there is a reduction in how the temp feels on your skin. There are grafts that will show you the numbers of the wind chill. I have a feeling that this is true even if the air is 80 degrees. Therfore in an office I would leave the heating fan on and take advantage of the wind chill.