a normal openvpn installation does not install client.conf/server.conf files, except for sample config files in a special directory (e.g. /usr/share/doc/openvpn-2.X.Y)
which web admin GUI are you talking about:
web based admin console under advanced VPN settings
If your version of the NetworkManager is new enough then you can export the config file - it will be (almost) the same as a regular openvpn config file. For older versions (< 0.8) the format is quite different.