Normally running the furnace fan constantly to reduce humidity during
the summer is a bad idea. I did it in my house as a test, using data
loggers to measure and record relative humidity. When I ran the blower
constantly one summer, it raised the relative humidity 10% to 15% over
letting it run just when the compressor run. TThe extra relative
humidity is from water re-evaporating from the cooling coil and drain
pan.

But I live in Myrtle Beach, SC and humidity is a big problem here.
Since you are measuring the humidity in the rest of the house and it is
staying at an acceptable level. I would say that it is OK to continue
to do so. Just continue to monitor the humidity in the basement and
house. Do whatever works in your climate and your house. The furnace
blower should use less electricity than a dehumidifier.

Stretch