well..if it had a type of buffer underrun support, such as "burn proof" or "smart link" or wahtever they want to call it then you are fine atleast when it comes to worrying about errored discs.
Oh, and I used to use a 133mhz Pentium Machine with a 8x burner at my dad's work back in the day, and I constantly burned at 8x while surfing the net and downloading game demos ALL at the same time...my burn times were also within what you would expect. Though the machine did have 128 megs of ram, but still you should be fine...some guys there days act like you need a freaking best of a machine to do anything.
But at the same time my guess is you'll be limited to around ~20Xish give or take a few but still not bad at all