You can leave the 1117's input open, and of course no current will flow out that way. But its ground is still connected, and voltage applied to the output pin could potentially result in current flow to ground. In fact we know a little current would flow because of the resistor divider on the output that regulates the output voltage normally.
I suspect very little current would flow back through a 1117. But if you can isolate it, you can measure that by applying the new output voltage to that pin, with the input open, and seeing how much current flows. You might start using a 1k series resistor to prevent very large current flows, but when it turns out there are none, you could just connect directly and measure the current flow.
I don't have a 1117 handy to test with, but someone here does, and could do that test. In my experience in general, if very little current flows back through the 1117's ground, with input open, then no damage will result, and a bypass reverse diode isn't needed.