Can a diode prevent backwards current flow from a constant current source?
It would (for all intents and purposes - there is always some leakage). However, a more significant issue is the fact that it will also drop almost half of you AA battery voltage - and thus waste half of the energy inside the battery. There are two options to mitigate this: 

Battery protection circuits with some form of switch, such as a mosfet: These exist and use a circuit that will open a mosfet when power is applied from the output. 

Alternatively, you could just use a NiMH battery and allow the system to charge it.