Is it OK to vent a first floor bathroom with a fan and a duct running through the basement?
Most wall mount ventilation fans are intended to go thru an exterior wall to a cap.

Your plan will work, if you make allowances to support the duct away from the wall a bit, to make the initial turn down.  Use smooth duct and metal tape for sealing duct sections.
update Be sure to slope all horizontal runs of the duct such that they will drain any condensation to the outside.