Technically it should be possible. Configuration might be a bit more difficult because on every device you'll need to configure not only the IPv6 address of the server but also which network interface to use for reaching it. Some client software might not provide an option for that. It might also create problems later when you want multiple networks to reach your storage, because link-local addresses are not routable.
I would personally just use global addresses to keep things easy, and use simple firewall rules to block access to the storage network. If you really want private address I would recommend using ULA addresses over link-local for this purpose. Use one of the online ULA generators to get an almost certainly unique block, and use that. That way you can expand the number of networks, build a VPN for management etc if/when you need them.