If you plugged your shore power cord directly into your inverter then yes, all the outlets in your RV should have power. You would want to turn off your built in converter (battery charger) when doing this. You would also want to make sure your refrigerator and water heater are set to gas and not electric.
It sound like you've done this and don't have power. That's just basic troubleshooting. Check for power at the inverter, check for power at the dog bone adapter, check for power in the RV breaker panel, etc.
You do have a volt meter I hope. If not this is a useless exercise.