In general, I'd rather know the truth. Knowledge is better than ignorance.
A lot of good could come from such information. Knowing you were susceptible to a disease could lead you to take precautions that could save your life. Like if you know that you are at risk for a disease that is spread by a bug that often lives in cat's fur, you would be wise not to have a pet cat. Etc.
If you had a good idea when you are going to die, you could plan your life accordingly. Like if you know you are going to live to 110 in makes sense to be more concerned about having a good retirement plan than if you are going to die at 30. If you are going to die before your children grow up you could make serious plans to provide for them. If you have something you really want to accomplish in life and you know your time is running out, better do it now.
I am suddenly reminded of the person who heard a preacher ask, "What would you do differently if you knew that Christ was going to return tomorrow?" And he thought a moment and then said to himself, Well, I wouldn't mow the lawn, because what's the point of mowing the lawn if the world is going to end tomorrow?
That said, one can certainly imagine horror scenarios. Someone takes a test that finds he is "at risk" for some fatal disease. That doesn't mean he'll get it, just that he's more likely than most. But if he thinks of that as "I will die from this disease", he might make poor decisions. I can see things from "I'm not going to marry Sally even though we're deeply in love because it would be cruel to tie her to a marriage with a man whose going to die a lingering death", and so they both miss out on all the happiness they could have had; up to he sinks into despair and commits suicide.
Technically, the problem in those scenarios is not too much information but information that is misinterpreted. And wrong information is often worse than no information at all.
If a number of people were told, with absolute certainty, that they had one year to live, I suppose it is true that some would respond by making rational, intelligent decisions to provide for their families, pass on responsibilities at work or other activities, etc.; while others would sink into despair or go berserk. What would be the percentage of each? I don't know. If some people would take positive action based on such information while others would be irrational, is it fair to say that the responsible people should be denied this information because there are other people who would abuse it?
Side note: If everyone knew pretty closely when they were going to die, the life insurance industry would be destroyed. If you knew for a fact that you are going to live long enough to pay more in premiums than your heirs would receive in death benefits, than there'd be no point buying a life insurance policy. You'd be better to put the money in the stock market or some other investment. On the other hand, if the insurance company knew that you are going to die young and they would have to pay out more than they would collect in premiums, they'd never sell you the policy. Life insurance only works because both the insurance company and the customer don't know how long the customer will live. And that ignorance makes it possible for people who turn out to die young to provide for their families. Without that ignorance, it would be impossible to use anything resembling life insurance to provide for families of people who suffer untimely deaths. (There might, of course, be some totally different method.) It's an interesting conundrum, I think: a positive good to society comes out of ignorance. An entire industry that provides a useful service only exists because of what we don't know. There are many industries that exist to find information that is unknown or to share knowledge, but that's a fundamentally different thing. Life insurance depends on not knowing and never knowing, until it's too late.