Can a kitchen be cooled indefinitely by leaving the door of the refrigerator open?

No, although the short-term effect would be for the refrigerator air / freezer air to mix with and cool the air in the room.

The function of refrigerator is a heat exchanger; it removes heat from the inside of the fridge and pumps it to the outside of the fridge.

If we open the refrigerator door, it will remove the heat from the air that mixes inside, but then will exchange the heat back into the kitchen. That's why the room can't be cooled for a long period. In fact, due to waste heat, the room could become warmer once the refrigerator contents have reached room temperature.