The emulated EEPROM (which Freescale/NXP calls "FlexNVM") does indeed retain your data while power if off. A large block of non-volatile flash memory is used to actual store the data.
Like all EEPROM (real or emulated), if power is pulled during the very brief moment your code writes data, that particular piece of data could end up corrupted. If you need to guard against this, the best way involves using a pair of resistors to scale the power supply voltage *before* the input regulator to an analog signal you can read. Then you can check if the voltage is good, knowing the charge left within the capacitors will be plenty to allow the hardware to continue running long enough to complete the write operation.