The answer is no. To understand this more, we first have to understand how a refrigerator works. Refrigeration is a cycle and it involves five components of the refrigerator. They are:-
1.Refrigerant or coolant
2.Compressor
3.Condenser coils
4.Evaporator coils
5.Expansion valve
When you switch on the refrigerator, the electrically powered compressor compresses the refrigerant gas and due to the pressure, it heats up. This hot gas passes through condenser coils, which are located outside the refrigerator. As it passes through the condenser coils, the heat it released to the surroundings and cools down the refrigerant, while turning it into liquid form. As the refrigerant reaches the expansion valve, the liquid becomes gas due to sudden drop in pressure. Now the cool gas passes through the evaporator coils and absorbs heat from the food kept in the fridge. At this stage it becomes liquid and flows back into the compressor. The process repeats again.
You must have noticed that the back side of the refrigerator, where the condenser coils are located, are always hot. This is because the heat absorbed from the food inside the fridge is released to the atmosphere through the condenser coils. And when the door of the fridge is kept open, the evaporator absorbs heat, not just from the food, but the entire room and releases heat again to the room itself. So the process actually heats up the room.