Can Legacy Dual-Core CPUs Drive Modern GPUs?

This graph shows how the Q6600 stacks up against the E6850 when both systems are equipped with the GTX 660.

Here's the short, non-math version: A quad-core is significantly better than a dual-core for modern games. An overclocked Core 2 Duo quad-core is meaningfully faster than a stock-clocked variant.

Intel Core 2 Q6600 chips aren't available new these days, but Ebay has a ton of them, regularly priced between $50-$70. If you plan to overclock a Q6600, you'll want the G0 stepping (SLACR). Other quad-core variants are also available, including chips based on the 45nm Yorkfield CPU. Price and availability are obviously highly variable and the usual caveats apply when buying from Ebay.
Is a new CPU worth the price? I'd say yes -- especially if you've currently got a dual-core CPU in the 2.2 - 2.6GHz range. The combined cost of a used Q6600 and a GeForce GTX 660 should still come in below $300 while delivering far better performance than any bottom-end desktop you might assemble for that price tag.