Some research emerging recently from Australia suggests it does. They looked at age and cause of death of thousands of people and found that those in sports and performing roles, and even those in creative roles which were non-performing, died younger than those in jobs in business, politics and the military. (I assume this was military people in peacetime!)
The question is why this is so. You could think that life in performing and creative jobs could be uncertain and pressurized, but surely so is politics and the military. One difference may be that you tend to be alone or competing with others as a performer whereas in the military you are part of a team, all supporting one another. Even in politics, there is a structure, which can be missing for a performer, who may have bursts of work under high pressure and stress with uncertain gaps between them, with extreme highs and lows and the uncertainty of never knowing where the next job is coming from. For sports people, the pressure to excel and win is always there, with the anxiety that can accompany that pressure.
The report did not suggest why performers died earlier, but it tended to be from accidents, infections or cancer of one of their organs. Lung cancer from chronic smoking was far more common in performers, with 7% of performers dying from that disease as opposed to only 1.4% among professional people generally. Surprisingly, there was no mention of performers dying in significantly higher numbers from drug or alcohol abuse.
Fame itself, being constantly watched and judged, and the lack of privacy, might add to the problem of stress. However, the research looked at the type of work rather than fame specifically. For instance, some politicians are famous and some aren't. It would be interesting to find if the famous ones had on average shorter lives but this wasn't considered.
What is apparent is that being famous might be exciting, but if you want to live longer, choose a job that is secure, companionable and low-stress. Fame isn't all it's cut out to be.