not if you do it the usual way of interrupting the power to the 'fridge.
The refrigerator part of the Fridge/freezer appliance is cooled by cold air that is vented to it from the freezer. There is only one compressor system in a refrigerator. It is slaved to the freezer.
Once you slave that compressor to the RANCO control the only thermally driven directives will be from the temperature probe on that RANCO unit.
Might as well cut a hole or remove the partition between the freezer and the fridge.
I was thinking about doing a variation on this, exactly to retain the function of the freezer, by slaving the vent to the RANCO type controller. Slaving the Vent would leave the freezer intact while also regulating the fridge's temperature. It'd only require that you interrupt the hot lead to the vent motor and hook that to the RANCO controller. .