From what I understand regarding winglets, they are neither proven to be more efficeint or economical than if without, except for at a particular level and cruise set up.
So, again, from what I understand, at that particular cruise level and conditions they make the aircraft more efficeint and economical, but perhaps decrease those values getting to that level.
Hence, neither one way or the other.
If you stick something onto a plane and into the airflow you will 1. increase the weight of the total plane and 2. increase the drag, thats about my level of understanding.