Back to the original question the Converter will produce a DC output whether or not there is a battery attached in the system. The IOTA in our 07 was rated at 75 amps. I don't think I could pull 75 AMPS if I tried so little chance of needing to draw on the battery for a makeup source of power. Most of the rigs you see at a RV show do not have batteries installed. As others have pointed out if you only have AC providing all of your power losing AC will cause a loss of all power.
On the draining of the battery, unless the disconnect is opened you will have some loads that do not secure. The propane detector comes to mind as one. The CO detector and the smoke detector are powered by batteries. If you don't turn off your tempurature control unit that draws power. Even with all those loads secured a battery will slowly self discharge over time
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Bill and Lisa Rearick
2023 Grand Design Reflection 367BHS
2020 GMC SIERRA 2500 Denali, 8 ft bed, SRW, Duramax Diesel w/10 speed Alison Transmission.
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