Your computer will not blow up if there is no power, but your video card will not be able to run at full speed because it does not have enough power going to it. For my PC, I had to take everything off the line for my 6600GT, otherwise I would get like 5 FPS... ridiculous...
Anyways, you are most likely going to need a new PSU for that GPU, because I have a 400W 20A on the 12V rail and it can barely power my 6600GT (your card replaces mine
)