rpmerril,
Yes, It is possible.. but be careful, Our fridge plus ancillary items draws about 2.5 amps on average.
2.5 amps x 24 hours = 60 amp hours per day usage.
If you have a single solar panel from the factory you can expect 10 amps at best during the middle of the day in direct sun with no obstructions. Given the varying sun angle and daylight hours you are likely getting less than 5 amps charge on average from the solar panel over 12 hours. Over 24 hours that averages to 2.5 amps or
2.5 amps x 24 hours ='60 amp hours of charge per day.
There you go! Charge maintained. However, this assumes a clear day. Given the cloudy conditions you describe I suspect you are getting even less charge than this, but you are also getting more hours of daylight this time of year so let's go with it.
If you are seeing 13+ volts on the batts they are likely under solar charge and thus that is not a reliable indicator of state of charge (SOC). You need to check the batteries when not under charge (after the sun goes down) and when the refrigerator has been off for at least 30 minutes (turn the breaker off to check). If you are still above 12.6 volts you are probably good to go. Less than that and you are slowly depleting them each day due to variation in the assumptions above. It doesn't take much to make these numbers go the other way!
I agree that in the best conditions it may be possible that the refrigerator could be left on with nothing else turned on in the summer (no one on the boat using stuff). However, I would confirm, what your average draw is, what sort of average charge you are getting from the solar panel, and what your actual SOC is before counting on it. The numbers can go the other way quickly!
Curt