Yes, accidentally leaving the refrigerator open can waste energy, even if it's helping your air conditioner cool down your house. While there might be some minor heat exchange between the refrigerator and the surrounding air, the energy consumption of the refrigerator far outweighs any cooling effect it might have on your home.
Refrigerators are designed to maintain a colder temperature inside than the ambient temperature outside. When you leave the refrigerator open, the cool air inside will escape, and the refrigerator will have to work harder to maintain its desired temperature, leading to increased energy consumption.
The small amount of cooling that the open refrigerator might provide to the room would be negligible compared to the energy it consumes to keep its contents cold. The net result will still be a waste of energy and an unnecessary strain on your refrigerator's compressor, which can lead to increased wear and tear on the appliance.
If you want to cool down your home efficiently, it's better to rely on your air conditioner to do the job. Make sure your refrigerator remains closed properly to avoid unnecessary energy consumption and keep your perishables fresh.