Now I understand your question, thanks for the clarification. I am also not familiar with a cold plate. But I think we can view this the same way we view a refrigerator with an external water dispenser. The water enters the fridge warm and comes out cold. Simple, right?
Inside the fridge is actually about 30 feet of plastic tubing coiled up and laying on the bottom, typically under the fruit and vegetables drawers. Now, when you draw water, it’s cold, but not as cold as one would like their beer. That’s because the coil is located on the bottom of the fridge. If that coil were located on the top, where you would normally keep a bottle of your favorite brew, than the water would exit the fright very cold, like that cold bottle of beer.
So, the answer to your question: YES, It will work providing the coil is located at the top of the fridge and your fridge thermostat is set to about 36-38 degrees. Note, I say “coil”. Again, I’m not familiar with a cold plate nor the thermal conductivity of this product.
Now, the length of your coil you use would be relative to the quantity of beer you wish to draw before allowing time for fresh (warm) beer to cool.