No, the TPS62730 is not essential for the CC2540. The CC2540 can run directly from any power source providing between 2.0 V and 3.6 V.
The TPS62730 is a 2.1 V buck regulator often used to reduce the power consumption of CC2540. The digital core and radio inside CC2540 is running off an internal 1.8V LDO, so by using a high efficiency external regulator you can reduce the power loss in the LDO (or in other words: increase the efficiency).
/Fredrik