I also pull my batteries (6 volt) during winter storage, but typically don't apply electric power to the trailer while in storage. According to WFCO, unless you're going to operate a leveling system, slides or other "heavy use" electrical component, you don't need a battery installed.
Here is the WFCO FAQ response to the question:
Does the converter need a battery to operate?
No. The battery works in conjunction with the converter to supply DC power to the RV. A battery is typically only necessary if you do a lot of dry camping or have slide-outs and/or a leveling system.
Here's the link to the entire FAQ section:
http://wfcoelectronics.com/faq/