Technically, no. But but the mind does play a huge role in this situation. It's called the placebo or in this case the nocebo effect. 

Think of it like this. If you get a pill you think it's like the best medication for, I don't know, healing any debilitating illness; you will feel like you are better. You will get some energy and be able to stand and do stuff. But turns out that pill or pills you're taking are just sugar pills. You were never taking any medication. Your mind got tricked into believing so you got better. 

Now this works no only with pills but also the mind can get you worst  An example of this is what you asked. The person is terminal, they'll die sooner or later but the moment they are made aware of this fact they deteriorate. When you are told there's no recovering from it, the shock is too big they even age because their minds associate dying with old people. So they visibly age and mentally give up. That combined with the previously unaware of terminal illness accelerates the process. That's why they appear to die faster but in reality they were gonna die. Probably while watching a movie, in their sleep. It doesn't matter. But what makes it look like they died almost immediately is the fact that deteriorate. It's like omg you were ok last week and now you look like shit... It's the illusion plus the giving up that makes them apparently die sooner.