Yes you shouldn't get much drop with three parallel cells.
Careful with that setup. Don't space out when installing the cells and install one backwards or one that doesn't have the same charge level. You have no protection for that. You would need to fuse each cell to provide protection.
The problem with copper is it corrodes pretty fast which will interfere with connection quality. What you can do is buff out the contacts then apply some Noalox. That will keep them from tarnishing.
Silver has the same problem as copper, it tarnishes pretty heavily, but not nearly as fast as copper. It will work better than copper in that regard, but will have the same problem, brass too. Contacts normally have to plated with a corrosion resistant metal like nickel or more exotically rhodium.