Did you just recently watch Big Fish? That guy learned how he was going to die and used it to his advantage.
In this case, it's easy to say no because you don't want to think about it, you'd rather it be a surprise (in a sense), and you don't want to live a life of fear. But, I think knowing would make you feel all the more liberated. Even if you found out you'd die in a week, wouldn't it motivate you to make the most of that week instead of doing what you normally do and dying completely by surprise?
Also, if you knew you would die farther down the line, then you could be certain that no other things would kill you, thus you could live without fear of consequences which is usually what prevents us from experiencing life to it's fullest. It seems pretty clear to me: accept the offer and prepare to make the most of the time you have instead of living a life of reticence.