Depends on the style of the unit. I have a standalone freezer, and a small dorm fridge that have the condensing tubing just under the exterior shell. Adding extra insulation to the outside shell of these units will not work.
I also have a dutch door style fridge/freezer frost-free where the condensing coil is underneath the unit, and the air is circulated through the coil by a fan. This unit needs to have the coils brushed and vacuumed frequently to prevent dust build-up from blocking air-flow (dog hair removal). There is a heat strip arround the door that is used to prevent condensate build-up, and a drip pan under the freezer unit, near the fan, that catches all the melt from the frost-free cycle. This unit might function with additional insulation arround the top, sides and back of the fridge, but I think the doors, and door seals are where most of the heat infiltration would be.
Questions to answer about this style of unit - will the extra insulation prevent condensation build-up on the outside of the cabinet? That is what the airflow gap is suposed to do. - Can the exterior heat strip, and the defrost cycle be disabled to conserve energy (battery drain)? - Are there issues with defrost cycle melt-off splashing out of the catch pan?
I think keeping a unit like this filled, so there is not as much air exchange when the door is opened, and having the contents acting as a thermal mass, would be just as beneficial.
I'm thinking a very old style 1950/60s fridge with an external condenser coil on the back, and a door latch would be optimal to modify for this application.