It would appear to be the case, as recent pictures of President Obama show significant graying of his hair when compared to pictures of him taken before he took office. However, being stressed out plays a minor role in the premature graying of hair. The premature graying of hair depends more on genetics and family inheritance (McDonough and Schwartz, 2012).
However, extremely stressful jobs like the President of the United States can accelerate the rate of premature graying.. So it is worth handing stress so that you don't feel the negative effects of anxiety and stress on your body, such as premature graying of hair and hair loss.
Premature hair graying. McDonough PH, Schwartz RA. Cutis. 2012 Apr;89(4):161-5.