Can a fridge, left open in a closed room, be used to cool the room?

No. Instead it will heat the room. Under normal circumstances, the heat from inside the fridge is taken out by the compressor and let out in the air behind the fridge. As a result, the space inside is cooled. If the fridge is kept open in a closed room, the chillness coming out through the front door of the fridge is cancelled by the heated air coming from behind.

 Apart from this, in any electrical appliance, a part of the electricity supplied is wasted as heat because of the principles of thermodynamics. This heat will raise the temperature of air inside the room.