Yes, Volkswagen's plan to invest $600 million in Tennessee plant will help the South's economy. Any time you take an amount of money and spend it somewhere else, you will help that local economy. There's no reason why $600 million new dollars, and the jobs that come with it, would do any harm to Tennessee.
The South needs to get more industries and exposure in order to generate revenue for their own development as well as for generating employment in the local areas. $600 million is a huge investment, the risk is high and so will be the result. More such project should be launched soon to see a whole developed South US
Tennessee is a state with many rural areas, and has been hit hard by the recession. A substantial investment of this size will have very positive effects on the South's economy not only through direct job creation but also through the positive spillover and secondary jobs that will be created in other industries.
VW investing $600 million to expand a plant in Tennessee speaks volumes to the American car industry. This will directly affect job availability throughout the south. Construction at the plant and the jobs working inside the plant after it's expansion can only have a direct effect on the economy during and there after.
The singular investment of one company in the South cannot change the economic trends of several years. This investment alone will make no difference, however, if this investment is the consequence of positive change in the area which is causing companies to believe that this is an area where they will be able to thrive then this is a very different story. However, I doubt this is the case here.