Some cheap OEM converters say in their user manual NOT to operate the converter without a battery in the circuit. The battery helps as needed with large loads like the slide out motor, also provides a stable voltage source to electronics.
If the trailer is big enough to require brakes, it also is required to have a battery onboard and a breakaway switch for the brakes. As Barney said, this is covered by state laws but every state has this law in some fashion.
Since you camp with hookups, you don't have to worry about battery capacity, you can get a 12v deep cycle/marine battery at Costco for $89.