You can, but wouldn't we expect them to be correlated? E.g., better health and less disease should lead to a longer life (as we assume all non-health related deaths to be random and not correlated to health)
Take two groups of people who live active lifestyles in non polluted areas, who don't smoke and don't have any other health issues (including mental health issues because a lot of them are correlated with a shortened lifetime). Give placebos for one of these groups.
This study would help a bit, but would be impossible : we don't have enough people who live this lifestyle and are available for long testings on multivitamins. They may also change their lifestyle, get into an accident, develop mental health issues, travel...Which would poison the results.
I think no one should take multivitamins expecting to live longer. Take them for the other proven benefits - they counteract deficiencies, that's all. My blood tests already show this, I take a blood test before an Iron Supplementation Cure and after, the benefit is clearly visible on the test.