Asynchronous USB DAC's do a great job of lowering jitter from the USB. They do this by basically controlling the clocking of the signal. Many DACs use re-clocking techniques on S/PDIF signals. So, if the USB to S/PDIF interface delivers bit perfect data to such a DAC, it seems that re-clocking in the DAC should be able to produce jitter similar to that on the various asyncrhonous USB DACs. The OP's Berkeley DAC is a high end DAC which, according to the Berkeley website has "Advanced input signal jitter rejection". So, it is quite possible that a S/PDIF or maybe a AES output from a PC coupled with the Berkeley DAC may be able to produce jitter figures as good as the aysnchronous DACs. The Berkeley DAC gets great reviews both in terms of sound and in terms of features.
Chuck/Johnny - you might want to check of the system that Goodwin's High End has put together to drive the Berkeley DAC. It uses solid states disks, has no fans and uses other means to make for a really quiet system. Last I knew it was only using XP and a 16 bit (not 24 bit) Lynx card but they may have updated it. I am not necessarily recommending that system, but it is interesting to look at what they did.