Not so. Inverters switch approximately 20,000 times a second. The on / off times are selected to generate a 60Hz sine wave. So switching it high and low intermittently will have no discernable effect on your inverter.

But to answer your question, oddly enough there is a device that can do this. They are used in hotel and dorm rooms. The device is connected to the microwave and refrigerator. It is designed to shut off the refrigerator when you turn the microwave on. This limits the power from the building.

If you plug a 1000W space heater into the refrigerator and your other load to the microwave input you will get what you asked for. I don't recommend this but it answers your querie.