Does a duo processor mean double the power?

The processor is an Intel Core 2 Duo T6600 (2.20GHz/800Mhz FSB/2MB cache). When it says duo does that mean the GHz are doubled or what? The laptop I want needs to be cheap but still has to able to handle video games. The video games I want require a minimum 2.4 GHz. Will I still be able to play using this processor?