As with any hypermiling technique, when applied properly, it would save no more fuel than simply using the intersection's traffic pattern to your advantage, timing the intersection for the left turn, as you would for straight travel, so you can minimize stop and go.
For the average driver, who is
reactive, as opposed to hypermilers, who strive to be
proactive, minimizing left turns can, and probably does save fuel. Unfortunately, it takes planning, which most do not and will not do. Planning takes time, and people don't realize that you must invest in order to save.