I highly recommend considering using the 16 bit samples for tracking...and the 24 bit for rendering.
I have a G5 dual 2.5 with 2.5 GB Ram, SATA internal drive, and even it can be smacked around a bit too much with the 24 bit samples. Once I paid the little bit extra for the 16 bit samples, it made the library much more playable for me. Granted, I work it pretty hard, but the 16 bit allows me to take it much further!
Performing with TBO is not CPU intensive particularly it just uses a fair amount of RAM. That dual core system you mentioned will do it easily. The main issue is disk speed - that will determne how fast the instrument is to load and how many notes you can stream. A 7200 RPM ATA drive will do it, a 10k RPM would be faster at loading the library.
I use TBO (24bit)/Kontakt2 on an AMD X2 4400 with 2GB RAM and it works without any problems, although sympathetic resonance scripts can put a quite high load on disks and to some extent the cpu. From what I've heard the benefits of using Kontakt2 on dual cores seem to reduce quickly as you lower your latency (eg. one of the developers of Kontakt2 advised against using latencies as low as 3 ms if one want Kontakt to take full advantage of both cores), which might be good to know. I agree with MMcd that you probably should worry more about disk load than cpu load.
I probably should have noted that I am using HALion, so that could be (is!) my problem. You guys have given me yet another reason to jump onto the Kontakt wagon. I downloaded the demo and noticed a rather significant improvement in efficiency. Kontakt was not hicupping like HALion was. Best of luck to you.