Can a AMS1117 fixed voltage regulator be used in a reverse biased way?
Using an internal "feature" of an IC for an unintended purpose may always work, or sometimes work, or stop working in un-understood circumstances.  

In this case, adding a Schottky diode across the regulator from Vout to Vin to take the 'reverse' current would be an effective, cheap and sensible solution. 

TI &amp; Nat Semi datasheets contain references to an internal protection diode.
A sample Asian datasheet did not. They still MAY exist.

TI datasheet
Section 7.4 page 12. Figure 13  

Natsemi data sheet page 10 fig 4

Both say:

Under normal operation, the LM1117 regulators do not need any protection diode. With the adjustable device, the internal resistance between the adjust and output terminals limits the current. No diode is needed to divert the current around the regulator  even  with  capacitor  on  the  adjust  terminal.  The adjust pin can take a transient signal of±25V with respect to the output voltage without damaging the device. 

When a output capacitor is connected to a regulator and the input is shorted to ground, the output capacitor will discharge into  the  output  of  the  regulator. The  discharge  current  de-pends on the value of the capacitor, the output voltage of the regulator, and rate of decrease of VIN. In the LM1117 regulators, the internal diode between the output and input pins can  withstand  microsecond  surge  currents  of  10A to  20A.  

With  an  extremely  large  output  capacitor  (≥1000  μF),  and with input instantaneously shorted to ground, the regulator could be damaged.In this case, an external diode is recommended between the output and input pins to protect the regulator, as shown in Fig 4 (13)