Is a microwave oven an inductive load?
Present common microwave ovens run by  capacitive AC pass Inverter power supply which makes it very energy efficient , doing away with heavy Inductive primary transformers , and bulky capacitors as also other higher ampere usage components which brings me to my answer I would not plug older transformer type units that will  quickly drain any system like you mention , UPS Supplies intended for computer backup is less than an adequate choice for this reason , So no to older appliances , further more A modern DC- TO - AC Matched to a Modern Oven ( microwave ) works just fine for a quick dish , Hope I made some sense ...!