If you are plugged in during that period the inverter should not be necessary to provide power to the TV and receiver as it should be designed to pass A/C when plugged in and act as an inverter when you are not connected to shore power.
If you are dry camping and want to keep the TV and receiver running then you must leave the inverter powered on. This is not at all a bad thing unless you don't have enough battery power in reserve to deal with the constant 25W draw from the receiver and a minimal amount more for the hard drive.