I am a bit surprised to hear; the fridge on my 330 cools almost immediately and from my experience doesn't add enough additional demand to draw batteries (four Grp 27, flooded) down too far overnight. I have breaker/switches on the AC/DC panel. I Think I recall working on an inverter under the fridge, but that just doesn't sound correct. Could be I'm confusing with TV cabinet and inverter located there.I am recalling from my old 2004 boat that refrig could be turned off by turning thermostat to 0. Otherwise there usually is a separate switch on breaker panel for the refrig as it is a big power hog and seldom used.
It takes too long to get cool when going out for a day and unless you have a shore power connected you cannot leave it on for any period of time, hardly even over night.
H