I have to use an OpenVPN network to work from home, and I occasionally have problems getting DNS to resolve. The problem comes and goes, and I can't reproduce it reliably.
I took the OpenVPN config that my employer provided and fed it into the "Import" part of the VPN tab in the Network Manager settings (after installing
network-manager-openvpn, of course).
The DNS servers automatically provided by the VPN did not appear to work reliably. so I went to the "IPv4 settings" tab of the VPN settings and changed it to "Automatic (VPN) addresses only" and put the search domain and servers in by hand. However, if I go to "Connection Information", I still see my system dns resolvers listed, and I cannot resolve anything that isn't on public dns.