A question for you would be why you are using a cold plate system? Is the volume of the event that low that you can use a cold plate? If you are dealing with high volume, use a coil system.
As to sandwiching the coil with ice - the ice on the bottom of the cold plate will eventually disappear since through the temperature transfer the ice will melt. Now if you check the ice after the system has dispensed beer for awhile and physically pulled the plate out and rebuilt your sandwich, that probably would be ideal.
Also, always fill the system with beer first prior to filling box with ice.
Scott Zuhse, Instructor
Micro Matic Dispense Institute