Battery Charging

Can anyone advise on the operation of the charging system on the 36cc, I think it is a Dolphin Charger ?
Charger appears to come on whenever connected to shore power and AC outlet breaker is on.
If I want to leave power on over winter for heater/dehumidifier what happens to batteries - do they fry ? Am I best rigging up a separate shower supply and not plugging into boat ring main ?