Economists Jonathan Klick and Thomas Stratmann find that it does.  In the latest issue of the Journal of Law and Economics, they write:

In the face of rising rates of diabetes, many states have passed laws requiring health insurance plans to cover medical treatments for the disease. Although supporters of the mandates expect them to improve the health of diabetics, the mandates have the potential to generate a moral hazard to the extent that medical treatments might displace individual behavioral improvements. Another possibility is that the mandates do little to improve insurance coverage for most individuals, as previous research on benefit mandates has suggested that mandates often duplicate what plans already cover. To examine the effects of these mandates, we employ a triple-differences methodology comparing the change in the gap in body mass index (BMI) between diabetics and nondiabetics in mandate and nonmandate states. We find that mandates do generate a moral hazard problem, with diabetics exhibiting higher BMIs after the adoption of these mandates.