Yes, copper is very effective at binding H2S and Mercaptans, so it will help reduce sulfur odors. It will also bind sulfur containing aromatic elements that may have a positive contribution, like thiols (some of the aroma elements in Sauvignon Blanc wine which can also be found in some meads). So copper can strip out some good aromas. Copper and Iron ions can allow hazes to form (particularly protein haze), and they may facilitate oxidation of wines.
Copper can be very useful, but like a lot of things, I like to use it only when necessary, and when the benefits outweigh the potential harm.
Medsen