FYI boiling removes chlorine but your other worry are chloramines because they don't boil off. If you use the campden tabs though you should be set.
I am really skeptical of using copper. I have an easy siphon that is just a hose attached to a copper piece with a marble in it. When I clean it with starsan, the rinseate smells of metal and it is pretty strong. Copper is probably being dissolved into copper sulfate plus what ever the oxidized copper does since it makes it nice and bright (strips the oxidation layer off). Copper is fairly reactive in comparison to stainless steel.
Besides the flavor concern....how many people are using food grade copper? Even if it is certified, I highly doubt it is certified for boiling temps. Stuff leaches out of copper so I am with you on your skepticism about it adding flavors but I have brewed beer that tastes just fine with a copper chiller so I don't know.
Let me ask you this...does the wort chiller seem polished or brighter after chilling your brew? If so, there very well could be copper oxides dissolved in the wort.
On the fip side, yeast is apparently supposed to take that stuff in and filter it out. I think that there is research about yeast absorbing metals but I have only heard about it, not actually read it so I have no idea if it is true.
I think that you should go with stainless steel equipment if you can. It is well know to have hardly anything leach out of it. When I can afford it, I want to upgrade to a SS chiller but daaaaayum, they are $$$. Chilling your pot in an ice bath doesn't take too much longer if you constantly stir both ice bath and wort...it's a pain but if you think you have a copper issue...it is prob the safer road.