John,
First, just to let you know most plated metal components are not coated with something else to help kick up the shine. The shine from the components comes from the same thing as finishing our work, the finer I sand/buff/polish the item the higher the gloss. So the base part before plating needs to be buffed to a high polish first as the plating process just like our finishing will highlight defects in the prep work.
Now to the meat of your question. Simply put, it will always cause a problem. But before I scare you off, it depends on how much of a problem you will have.
Also, please bear with me, it is a hard question to answer without a bit of backround, don't run away yet.
Whenever you put two dissimilar metals together you start a small reaction that usually goes unnoticed for a very long time. What you get is a redox or electrochemical reaction, think of it as a small battery. All metals (or any material for that matter) have a base electronegativity or ability to give or receive electrons. The greater the difference in the electronegativities, the more exciting the reaction. All metals if dissimilar, when put in contact together will begin passing electrons from one to the other and the process of corrosion begins. How much and how fast the corrosion takes place depends on how different in electronegativity the two dissimilar metals are.
This dissimilar metal corrosion is the reason that you do not see many old aircraft or NASA spacecraft around. These were engineered with top performance in mind, not long term survivability. There is all sorts of dissimilar metal contact and as such, many of the old planes and NASA's rockets are falling apart due to corrosion.
As an extreme case of how different electronegativities can be demonstrated. When you place Sodium in Water, the sodium has a low electronegativity and essentially, forces its electrons into the water, all the while, flaming and sputtering and spitting.
Now most of the metals and platings we deal with in penturning are close enough in electronegtivities to not really be a problem. You will not see dissimilar metal corrosion in 5, 10, or 20 years. What I cannot say is that it will not happen, it will happen but in most of the cases, not in our lifetimes or a few generations after.
Sorry about the long treatise, but I was hoping to explain a bit more thoroughly in effort to give a bit of understanding not just an answer.
Hope the chemistry didn't scare anyone off.
Brian