msp430 and LiFePo4 cell as supply
If you're confident that the battery voltage remains within the MSP430's specs you don't really need the regulator, but I would recommend to use one to have a clean power supply voltage. In any case, be sure to have a look at other components the MSP430 connects to. For instance when you drive a MOSFET the gate voltage may be below pinch-off and the FET won't do its job.
(I don't quite remember the specs, but I once tested how low the MSP430 would go, and found that it still worked at 1.3V. Don't take this value as a reference, though. Always refer to the datasheet!)

If you want to measure the battery's voltage you'll need an ADC reference voltage that's independent of that. For instance use an LDO to create a fixed ADC reference voltage of 2V, and divide the battery voltage by two before applying it to the ADC (to make it lower than the reference)