Even with battery power, the datasheet recommends 1uF capacitors. 100nF will not be enough.
What current do you want to get from the stabilizer? At low currents ( up to 100mA), the stabilizer losses will be less than 100 mV, and everything will work. However, at current, close to 0,5A, the losses can increase to 0,5-0,6V, and the battery will not be used efficiently.