You can use the same board. The input voltage range for the regulators used is -0.3 V to 18 V.
Say you feed a 3V battery input into the board: Since the board has LDO regulators with a 3.3V ouput, what would be the effect? How is the LDO regulator affected when the input volatage is less than the desired output volatge? Even if it works, is there effciency issues?