Ted is certainly correct about using a shunt based battery monitor to answer your question.
I presume your question is will your existing battery run the fridge during the non sunlight period for 24 hrs. I can answer that one right now, no. The better question is how much battery capacity and how much additional solar will it take to keep your fridge running for 1,2,3....days.
But if you tell us the exact make and model of your refrigerator, I can make a decent guess.
David
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