Yup it's definitely useful to dig down a bit around the deposit in order to unearth all the copper. Be sure to use the Antler Pickaxe for clearing away normal ground and using better pickaxes on that actual deposit - or have a nearby workbench/forge/portal for repairs with some chests for storing stone, copper and mob drops in.

edit: Use the portal for moving non restricted resources before running back with copper, tin, etc... Stone is extremely useful.