I have a Pentium D 2.8ghz, same model as yours but a lot slower. When I first got TS12 I had an ATI X-550, very similar to the X600. It ran, but not very well. I've since replaced the video card with an Nvidia 8500GT, so it runs a little better but my 2.8ghz CPU is still a bottleneck slowing everything else down.
So my guess is it will run on your system as-is, but spending $50 bucks or so for a newer faster video card would be an excellent idea. Check your power supply wattage, if it's less than 500 watts that will limit the class of video card you can use.