One possible issue is that the input voltage must not exceed the analog reference voltage, so if you reduce the analog reference to (say) 200mV you would have to make absolutely sure that the voltage you're reading could never exceed that.
Never exceed sounds like a safety warning which does not apply in this case. The analog input pins have an electrical damage safety warning if an applied voltage is higher then Vcc +.5vdc (so call it 5.5vdc) or less then ground -.5vdc. And that is regardless of what reference voltage value you are using, internal or external. What happens if your input voltage is higher then whatever reference voltage is being used the value returned will be 1023 for any voltage higher then the reference voltage. So for example, if you are using the internal 1.1vdc reference voltage then any voltage applied to the pin between 1.1vdc to 5.5vdc will return the same 1023 counts from the analogRead() function.