You can use 7.2, but it will stress the reciever. Servo's work best on 6V, but they will work fine on 7.2. The problem isn't so much with the 7.2V, it's the peak voltage that can be significantly higher than the 1.2V per cell that the pack has printed on it.
Tamiya ESC's have a BEC (Battery Eliminator Circutry) voltage of 7.2V. Those 4cell packs are alright, but the "AA" cells they use wear quickly and are a bit heavy and tall for practice use. Get a good quality NiMH cells in a 4 or 5 cell configuration and stick that in your car. A peak detection charger with the potential to charge at 1A is also required so that you don't damage the cells.
Why do you want to replace the BEC wire on your ESC with a 4 cell battery? Radio Priority Circury is standard on every ESC since about 1998, and it was still very popular before then. If you are using a mechanical speed control that uses a servo to operate the throttle then you may benefit from a separate pack because it will keep the car from running away when the pack gets low. An MSC is not an ESC. An MSC uses a servo to operate a switch with several resistors that help dissipate extra voltage. An ESC is often a small box with several heatsinks. Higher end ones may have a capacitor. Make sure you have an ESC before you go buying a separate pack, because if you are still using an MSC then it's better to save up for an ESC and dump that crappy little switch. ESC's are infinatly better.