Blizzard has confirmed that Group Finder & Dual Specialization are coming to Classic Era servers. Here is the blue post from Community Manager, Kaivax:
Classic Era
When making your decision to transfer, please consider that the Group Finder tool and the Dual Spec feature will soon be added to Classic Era realms. This means that new and existing characters on Classic Era realms will have the option to learn Dual Spec. At the same time, the rulesets between Anniversary Hardcore and the original Hardcore realms will be aligned. This means that the original Hardcore realms will receive Dual Spec, Instant Mail, and the Dungeon Finder tool.
No other changes are planned for Classic Era realms or Hardcore realms as part of this update.