If you have the original Univolt converter.......YES! That device requires the battery to act as a voltage 'filter' for the high VDC output of the Univolt.
If you replace it with a modern 'switch mode' type converter like a Parallax , they will operate without a battery in the circuit and provide a continual 13.6 VDC for your trailer's DC circuits.
IF you ever take the trailer on the road, you WILL be required to have a battery that is capable of operating the trailer brakes in the event of a disengagement from your tow vehicle.