Under 'normal' conditions, the copper will corrode.
Remember though, only SS in the passive state (usual) is more noble to copper. SS can become active & corrode if the surface oxide passivating film is disrupted by the presence of certain ions or acids. A study of nobility inversion in galvanic corrosion in the Cu-316 SS system caused by Fe(+3):
One conclusion (with which I am sure all will agree):
"From the practical point of view, any galvanic contacts of stainless steel, carbon steel and copper in water are undesirable."
For more information on preventing all types of corrosion when using stainless, see