There's more than a few pre-built pc's that have Delta or Seasonic OEM psu's, both of which are extremely good for a grey box, but there's far more that have old group regulated designs that barely meet the requirements to be called a psu. 300w rating is no indication that you'll actually get anything close to that, and realistically you'd really be far better off with a 400w unit. If you got lucky with a Seasonic or Delta 300w,then that would work, but any of the others would be a serious gamble.
It's cheaper to purchase a $40 psu than replace a $100 mobo or a $300 video card when the cheap psu shorts out and takes the components with it.