Whether it can work and whether it is the most efficient way of keeping things cold are not the same thing.
My fridge can make ice, And I bet it can also keep everything safer and colder for less electrical consumption to make soft ice, only to melt it.
Everyone always seeks to find a cheaper option for preserving food.
One must balance the initial cost vs long term cost, vs how long and how often their food preservation method needs to be powered.
Those wanting to do so indefinitely but generally long term, are best served by a 12v compressor fridge and enough charging sources to keep a battery relatively happy.
Also factor in the pain in the ass process of draining, perhaps recovering/ stinky cooler water, when instead one can open a door/lid and have dry possibly zip lock free food below 40F, and an ice tray above it.
YOu can certainly try the Ice maker, but you will be expending tome and effort of movng ice to your RTic, and draining water, and possibly dealing with contaminated water next to 44 degree food.
When i did th ecooler thing, andwould open the lid and shoot my IR temp gun around on the walls and food, much of the interior was well above 40F.
Shooting the same gun in my fridge right now reveals nothing above 35.5f, and I have a zip lock baggie filled with ice and two filled ice trays in my freezer compartment.
When my first fridge failed at 5 years of use, I had about 3 weeks of down time before getting another, and went back to the cooler. Even disregarding the issue of getting ice, going back to storing food in a cooler simply sucks in comparison.
To those who have never dwelled with anything but a cooler, Ignorance is Bliss. Those of us with 12v DC compressor fridges, have nightmares about coolers filled with ice, and wake up relieved.