The depravity path is it's own story with a slow decline towards a bad ending. So yes, you'll lose at least one girl.
But much like the Futa on Futa path before its release, it's tricky to fully explain what 'lose' means here without diving into details.
Just to be clear, this doesn't mean Milly’s getting cucked in any sense, it just means the story will begin to shift beyond her control.