The ONLY caution I will give with that converter is this> Insulate the positive battery lead(s) if is just one wire attached to the positive put the cable end in somewthing like an empty pill bottle and tape it to the cable so it does not come off.. If there are more than one tie them together (Bread tie or string) and .. A bigger pill bottle and tape it on. Make very sure it can not touch metal. Alternate is a short length of "Pool noodle" over the wire(s) to insulate them.
NOTE2 The converter should maintain the battery same as the "Trickle Charger" so I would not (did not) remove them.
Final note: Trickle chargers are generally bad Battery Tenders or Battery minders (Two competing products) which are computer controlled slow chargers (1-2 amps) are good. Some folks call them "Trickle Chargers" but they are way better.
When I "Stored for winter) I kept it plugged in Did not worry about the batteries as the Progressive Dynamics wizard took care of 'em.. I did use the rig most every day for an hour or two (one small room where I stuck my ham gear) but I could have done that w/o batteries...save for the day the power company failed to deliver.