I haven’t tried it, but I don’t see why not-- from the specs, 12 V, with typical power consumption at the wall of 2 W, means less than 166 mA at the Werkstatt. Could be a pretty small battery for a 2 hour gig.
Although the overall power consumption of the Werkstatt is pretty low (2W), there is a high initial current draw (hundreds of mA or maybe even an amp). This is likely due to startup of the many switching voltage regulators inside. That’s why the power supply for the Werkstatt supplies up to 1.2A, which is a lot more than is needed after startup. It would be hard to create a battery supply of 12V which can supply over an amp of current.
I’ve purchased 2600 ma AA batteries for Radio Control cars. Tower Hobbies, among other suppliers, carry RC batteries that may work for you. You’ll need a special charger, though.