I don't see any reason it shouldn't, although I think your CPU may be a little underpowered for high-speed burning. I would, however, always recomend that you go with an internal CDRW. When you have an external one connected to a USB connected with PCI it multiplies the number of things that can go wrong, and you'll likely end up with a plenty of coasters. An internal CDRW will also save you some cash, and that's always a good thing.
Edit: Also get some decent burning software. A few vendors package their burners with good software (like Lite-On), but for the most part you'll end up with a real pile of rubbish like Adaptec or Roxio Easy CD creator. If you want to do some serious burning, get a good one like Nero Burning ROM, CloneCD, Fireburner, or CDRwin.
My pick: Nero Burning ROM. I use it for everything but CCD.