If you are plugged into house power (or shore power) and the battery is hooked up in the trailer, and the converter in the trailer is working properly, then the battery will be receiving a "float charge" which will generally keep it charged without overcharging it.
Your question stated "Does the house power need to be on...?" - yes, the receptacle you are plugged into needs to be live (a lamp would light if you plugged that into it), for charging or charge maintaining to take place. And I'm talking about what you are plugged into here.
Rereading your post, I think you may be asking if any switches in the trailer need to be set to "on", specifically the 3-way Master Switch that lets you raise/lower the top, or turn everything but the refrigerator off, or deliver power to the interior lights, water pump, fans, etc.. It does not matter what you have on or off INSIDE the trailer. If plugged info shore power, you will charge/maintain the battery if everything is working right.
- Jack
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Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH, Progressive Dynamics Converter, Fan-Tastic Fan, LiFePO4 battery 12V DC Electrical System, SoftStartRV mounted on A/C
2024 F150 Platinum FX4 3.5L PowerBoost SCrew
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