Nope, in thermal transfers the highest rate you can get in a series of materials (with a uniform cross section) would be that of the material with the lowest conductivity.
In very loose terms the heat would rocket through the thin silver layer only to be slowed down again when it passes through the less conductive material.
Think of the silver as a 4 lane motorway, when you get to the aluminium or copper it will be like decreasing the number of lanes. You just can't get as many cars through (assuming all other things are constant e.g. speed )