depends on the psu, but its not likely. just dont oc, or change any settings. i very highly doubt it will blow up your computer in just a week. it will have a shorter lifespan, but 1 week is pretty rediculous. id feel pretty safe, although anything is possible.
You should be fine. Besides, you should have a 30 day return policy if ordering from newegg or tigerdirect. Typically that's the accepted time it seems. But I had a generic power supply running my computer for a while. However, when I upgraded from a 7300 LE card to a 9600gt, the old power supply when bye bye.