Can a bathroom fan be exhausted through existing gable vent?
I wouldn't exhaust the bathroom through the gable vent. 

First off, you'll be reducing the size of the gable vent. Whatever area you block with the exhaust duct, is a reduction in the area of the gable vent.  

Secondly. Depending on how the attic ventilation is designed, the hot moist air exhausted from the duct, could be drawn back into the attic through the gable vent.