How do you intend to power the outlets from the extension cord? Not with a suicide cord connection I hope.
If you mean to run things from the end of the extension cord that has its own outlets by adding a power bar to plug the TV etc into, then the only problem is to get that end of the extension cord inside the rig without leaving a door or window open so all the mosquitoes can get in.
To be able to keep the doors and windows closed against bugs, the shore power cord itself allows that by plugging it into the inverter outside (turn off the converter, fridge, WH on gas)
Perhaps you mean add an extension to the shore power cord which it is not long enough? Yes.