You could also place a diode on the regulator's input side to prevent the input LED from lighting up from any leakage currents. Just be sure to move the input cap to the regulatorregulator's input pin side. The TI version (LM1117) datasheet shows a similar example when using two regulators in a battery backup arrangement, (see figure 9-7). Also be aware that if passing a high current you could come close to the regulator's drop-out voltage requirements, so a Schottky type diode will be best to use in this case.