You said that you will not be using any extra power since the refrigerator will be running anyway, but that's not quite right. If you add objects that are at a higher temperature than the refrigerator's internal temperature the compressor will activate to compensate the difference in temperature, that means you will have increased power consumption in the end. The thing is, if your refrigerator is more efficient than your A/C unit, maybe you are saving some energy, but it is also important to note that some waste of cold air from the refrigerator will happen while you are transferring the bottles from the refrigerator to your cooler and vice-versa. There is also the power consumption of the fan, but the fan usage is not stricly necessary. Nonetheless, quite an interesting alternative idea.
