This would entirely depend on what you're planning to do with the system. If you're only planning to play older games (pre 2006 I'd say) then a faster single core would probably be fine. I'd look at the minimum and recommended requirements of the games you're hoping to use this for. If none of them mention a dual core CPU, then a single core is probably okay.
Also, keep in mind that excess GPU power may not get you higher framerates in CPU limited scenarios, but you will be able to crank up the anti-aliasing and resolution with little performance impact. A pair of 8800GTs for example would be extremely CPU limited by any Socket 939 CPU.
Almost forgot... any multitasking would obviously be seriously hindered by a single core. If you plan to use it for web browsing with a virus scanner, or other things while gaming, you'll want a dual core. Have you looked at Opteron processors? Some may be cheaper than their Athlon equivalents simply because they aren't as easily identified. There are a handful of single core and dual core models available for Socket 939 and they were popular with enthusiasts that had extra money to burn on CPUs back then... probably the same ones that went SLI. 🤣
Now for some blitting from the back buffer.