Yes, clogged fans will eventually kill your computer, in a sense.
Most new processors will slow themselves down if they get too hot, at least most of the pentiums I have seen.
On the other side of that, AMDs will fry themselves because they don't reduce the framerate when they get hot and consequently they die.
I just recently cleaned mine because going to the store to get some $4 air-in-a-can was just too much of a hassle
After about a year of letting it collect dust, I would suggest a hazmat suit or something to that effect.
Ick.