Hard data on students using W's to enhance their GPAs?
I've just done 15 minutes of moderately focused research, and found nothing.
It looks like in most exit surveys students claim to have dropped because of family or work conflicts, which may be true but is not the acute reason for the drop for your students.

A Google search for "drop and retake" finds dozens of recommendations like this for pre-med and other highly grade-motivated students. 

I'm rather intrigued, actually. If these students could be motivated to stay and get the grade, it would save the state a lot of money. And if they couldn't drop after Week 2, they might work much harder much earlier. 

I sense a possible research project...