Originally Posted by Old_Stevenick
I thought it would draw from the AC when plugged in.
So the Bullet's convertor is probably not lithium compatible.
Will it damage the battery as some articles say?
The fridge uses DC, which comes from the battery. If shore power is plugged in, the converter "instantly" keeps the battery up to charge, so in effect the AC is powering the fridge, but one step removed. Additionally, if you have no battery in the circuit at all (e.g., removed), the DC charging power from the converter is typically enough to run the fridge, lights, etc. all by itself without a battery (but not the slide, jacks, or big DC power hogs).
If the battery is sinking when you're on shore power, something weird is definitely going on. I'd take the time to determine whether your brand and model of converter is compatible with lithium batteries.