No the card shouldn't break...
But as with any power loss, you might lose data off the harddrives, if Windows for some reason is touching important data, like the registry.
Could be a small possibility of a surge to the system, if the PSU is really bad, but a few tests most likely won't hurt. and assuming that supply is OK, 400w is enough.
Since that PSU most likely doesn't have the special graphics card adapter, you should connect the adapter that comes with the graphic card, from two different lines, there's usually two separate coming from the psu, use both and you're safest possible..