The plus is that some older converter/chargers would cook the battery.
The minus is that the converter puts out more voltage (close to 14v) and the battery "mellows" it down. Dad used to burn light bulds out in a 2001 Winnebago with the battery disconected in the winter snow birbing.
The power coming out of the converter is not the smoothest and is fairly "dirty" and the voltage can sag and spike when loads are applied. The battery helps smooth out the voltage ripple and minimizes the sags and spikes. Some converters recommend not using it without a battery hooked up, I have not found a recommendation for the WFCO converter installed in newer Crossroads.