There was, and still is, one bizjet manufacturer who stridently purpoted that the winglets produced a forward thrust vector. Wind tunnel analyses that I studied seemed to verify this point, but.....there's no free lunch.
The thrust required to drive the winglet through the air somewhat exceeded the small net forward force generated, the result, a net total reduction in effective thrust available.
On the positive side, the winglets work well most of the time to alleviate drag, thus making the available thrust more effective, but countering this, the B747-400 under certain C.of G. conditions achieves improved Specific Ground Mileage with the winglets removed in about 20% of cases.