Yes, it can be done!
1. The voltage the device wants must be given. If it's 9V then you need* to give it approximately 9V. Too much will fry the unit and too little will under power it and it will work erratically.
2. If the device is takes AC, then you can power it with AC or, in most cases, DC. If it is DC, you cannot supply it with AC or it will almost surely malfunction.
*When giving an AC device DC, it is not always the same voltage. This depends on the internal circuitry. It's usually ok to provide a lower voltage but this can rarely cause some permanent damage in some devices.
The reason this works is that digital electronics requires DC. The pod is a digital device. The device itself converts AC to DC internally. If you are supplying DC to the converter, you get DC out. Hence, AC digital devices are usually AC+DC devices. If the device depends the AC for some specific reason, then it obviously won't work.
3. Since 12V != 9V, you will have reduce the voltage of the battery. This can be done with 4 diodes in series which gives a voltage drop of 4*0.7 = 2.8V. A current limiting resistor and a fuse would be handle to prevent potential disaster. You can check out the setup on some useless 9V device(Old junk pedal) if you want. Or just check the voltage and current across a temporarily load resistor that pulls should pull the same current as the device as listed in the specs.
I've powered some AC line6 pedals with DC without issue. In fact, all it required was modifying the plug to fit the jack.
4. If you create a rig to do this, you will need to make sure you ground things well in case of shock.