No experience with this one but putting plenty into Yachts with inverters and generators, Digital controls do not like cheap inverters and have a tendency to blow out if run on none sine wave inverters or generators.  Also some microwaves make you set the time before they will operate,pain in the but if you don't have continuous power . An old sharp half pint with the mechanical timer is your best bet if you plan to run on dc. and it fits under the sink. If you are only going to run on ac anything will work.
mike