In theory, it is possible to cool a closed, insulated room by operating an electric refrigerator with its door open. However, in practice, it is an inefficient and ineffective way to cool the room, and it could also lead to various issues.
When the refrigerator door is left open, the refrigerator's compressor will continue to run, trying to maintain a low temperature inside the fridge. As a result, the refrigerator's cooling system will be continuously working to remove heat from the room and transfer it to the refrigerator's interior. However, since the room is closed and insulated, the heat expelled by the refrigerator will have nowhere to go, effectively leading to a closed loop of heat exchange within the room.
This process will generate extra heat in the room due to the refrigerator's motor and compressor running continuously. As a consequence, the room's temperature is likely to increase rather than decrease, which is the opposite of what you want to achieve. This is also inefficient because the refrigerator is consuming extra energy without effectively cooling the room.
If you want to cool a room, it is better to use an air conditioner or a dedicated cooling system designed for this purpose. Air conditioners are specifically designed to remove heat from indoor spaces efficiently, and they can cool a room much more effectively than a refrigerator. Additionally, using a refrigerator with its door open for cooling purposes is not a sustainable practice, as it puts unnecessary strain on the refrigerator's components and increases energy consumption, leading to higher electricity bills and potential wear and tear on the appliance.