I think perhaps your understanding of "supporting IPv6" is a bit off track. Support would definitely not be to with your network interface itself; but rather on the kernel side as well as you interface driver side.
Thus for your "Box 1" to be able to ping "Box 2", you'd need to install a kernel that is IPv6 ready; and also make sure that your NIC drivers are patched to support IPv6. Obviously, this assumes you have a direct connection between Box 1 and Box 2. In this case "Box 1" would also "support" IPv6.
If Box 1 and Box 2 were on different networks where switches/routers/etc are involved; then all these devices would need to support IPv6 as well.
Have a look at this link which provides a healthy amount of info on IPv6 and Linux: http://tldp.org/HOWTO/html_single/Linux+IPv6-HOWTO/