No.
1, Remove the microwave romex from the main panel and connect to a 20a branch circuit in the sub panel.
2, New romex from the main panel empty 20a (or increase to a 30amp breaker) to the inverter input.
3, New romex from inverter output to the subpanel.
4, Move any additional circuits from the main panel to the subpanel if you want them powered by the inverter. Do not move the water heater, converter or air conditioner. These remain in the main panel. Fridge might be on the common GFCI circuit and need to be set to propane only or run separate circuit from main panel.