Can I use DC to run an AC device in some cases?
Any device that has a rectifier at the input and has no direct use of AC is a good candidate for operation by DC input. You need to determine the DC operating voltage and make sure that the capacitor charging current is not excessive. Some kind of recharge circuit may be required.

If the rectifier output has a capacitive filter, the DC voltage will be close to the peak of the input voltage waveform, RMS voltage multiplied by the square root of 2. You need to determine if mains voltage is rectified or if there is a transformer feeding the rectifier.