yes you can leave it on when connected to shore power. you will have a small transfer switch for you refrigerator. it may be internal to the inverter or it may be external. its purpose is to select either shore power, or inverter power, and pass one of them but not both though to the refrigerator. so if shore power is present the refrigerator will run on it. while doing this if the inverter is on it is basically in standby mode and is not providing power to the refrigerator. should shore power disappear the transfer switch will then connect to inverter power, if it is on, and pass it through to the refrigerator.
2015 cardinal model 3825fl
2015 dodge ram 3500 dually