Currently, OpenVPN requires that you have IPv4 configured inside the tunnel, which you can add IPv6 to as dual stack. What you do outside the tunnel is up to you (1).
That being said, here is your answer: OpenVPN 2.3 (and most likely 2.4) will not work IPv6-only (2).
Furthermore (3), here are two device types supported by OpenVPN: tun and tap.
Tun devices receive raw IP packets and give them to a user space program. In the case of OpenVPN this program encrypts those packets and sends them on to the other end of the tunnel where they get decrypted and sent back to the tun device on that side. In other words a tun device behaves like a virtual Point-to-Point network connection.
Tap devices use raw ethernet frames instead of IP packets. A tap device is like a virtual ethernet card - any packet sent to it goes through the tunnel and back up the ethernet stack on the other side. So an OpenVPN connection using tap is like a virtual ethernet bus with exactly two ethernet cards connected - one on each side of the tunnel. The downside of using tap is that for each packet 14 more bytes (the ethernet header) are used up, the upside is that we can use any protocol over it without having to think about OpenVPN support for it.
The first article that describes IPv6 support in OpenVPN using tun. The second one uses tap:
https://community.openvpn.net/openvpn/wiki/IPv6 (though IPv6 will not work with some mobile devices unless you are using 2.4+, see (4))
http://silmor.de/ipv6.openvpn.php (note that since this article was written, OpenVPN has enabled transport over IPv6—we are now in version 2.2+)