Ok to run shore power without battery?

I have a 2007 Komfort trailer with a WFCO ultra distribution panel model WF8955an with a 3 stage converter. Lately the fan in the panel has started running for hours at a time. I checked the battery and it is boiling HOT. We don’t travel, the trailer is plugged into shore power 100% of the time. Is there any problem with removing the battery and just having the 12v lights and bath fan run off the converter?