No, actually not accurate

1st, Dual Core is a general term that cover Core 2 Duo, Core Duo, and X2. Core 2 Duo is redesigned version of Core Duo. Of course it is better and faster. But power consumption is getting worse. New 34W vs. old 31W. Running faster and step down earlier is not necessary save you from battery drain.

On average, the Core 2 Duo is 15%-25% faster than Core Duo. Multi thread performance is also improved in Core 2 Duo, and of course with doubled cache. Honestly, Intel's cache design is really good.

2nd, you can't get doubled performance from Dual Core architecture. Softwares are mostly designed for single core and not optimized. Memory bottleneck will also largely slow down the process.

Basically, you will get about 20% speed increase just because a redesigned CPU and OS management in a spare core. You will experience a noticeable boost only when you scan virus and creating DVD at the same time. You will get slightly shorter battery life.