In my experience, PSUs are one of the most overrated components by hardware enthusiasts. A faulty PSU is dangerous, but a PSU that works well is not dangerous, and your system probably won't be putting out more than 330W at load. Check this out - http://www.anandtech.com/bench/GPU11/233 - a system with 560 Ti puts out 352W in Furmark (non-Ti has 20w lower TDP), and the CPU it was tested is i7-920 which has 30w higher TDP than A8-3870k.
So your PSU will be fine as long as it's not faulty.
That said, when buying a PSU, you really shouldn't be pinching pennies... and you shouldn't be buying prebuilt PCs anyway. PSU wouldn't fit? Why not get a new case instead of a crappy PSU?