I had a dead battery and my electric brakes worked. I did find that more worked properly when the battery was replaced. I haven't boon docked with just a battery but plan on it this winter. I am thinking of using a small quiet generator.
While the trailer's electric brakes will work without the battery when connected to the tow vehicle, the breakaway system will not work without the battery.
Agree with JLTN_James. It's important for the unlikely event where the trailer hitch has a catastrophic failure and the trailer heads off on it's own, that the battery is needed to activate the brakes.
1996 Suburban 4x4. 350, 4.10 3/4 ton
2005 Jayco Jay Flight 27BH
1986 Coleman Columbia Popup.