sometimes you have to, sometimes you don't. I dunno man... it's a very strange issue..
when I built a new pc for a friend, I just took the HDD out of the old box and put it in the new one, worked great.
When I did the same thing for my brother, windows would BSOD every time it boots up, and it was working perfectly fine on the other pc....
try going without a format, if you encounter problems, then format.