I voted yes. not because that's been my own behavior...when I was diagnosed with MS several years ago we told immediate family members who then spread the word (like wildfire) throughout the family.
However, I fully support an individual's right to make their own decision on disclosure. Let's face it, it can be very, very difficult to deal with a bad diagnosis, and if someone needs to cocoon themselves for however long it takes to deal with it, that's just fine.
Family members may not be happy when they do eventually find out about it, but that's not the ill person's responsibility. Whatever works for the patient is correct.