According to a study by David M. Cutler, Edward L. Glaeser, and Allison B. Rosen, the answer is yes.
From the abstract:
Despite substantial increases in obesity in the past three decades, the overall population risk profile is healthier now than it was formerly. For the population aged 25-74, the 10 year probability of death fell from 9.8 percent in 1971-75 to 8.4 percent in 1999-2002. Among the population aged 55-74, the 10 year risk of death fell from 25.7 percent to 21.7 percent.
