Funnily enough, some of the working memory training research was about driving! See http://www.gwern.net/DNB%20FAQ#seidler-2010

Let's see, looking at the abstract, the conclusion for driving specifically (emphasis added):

Although the results for older adults are preliminary as participants are still completing the intervention, they show transfer to the complex motor tasks and the driving simulator measures, particularly under dual task conditions. These results suggest that working memory training may be a useful intervention to improve driving in older adults, but has minimal impact in relatively high functioning young adults.

Maybe your WM really really sucks and so it might still be helpful?