If the ISP's DNS servers will resolve the VPN server's name to an IP address, everything should be fine -- it should work as follows:
- When you click "Connect", Tunnelblick (actually, OpenVPN) will use the ISP's DNS server to get the VPN server's IP address
- Tunnelblick will then connect to the VPN server
- After a connection has been established, the VPN server should then "push" a new DNS server address (possibly more than one) to Tunnelblick and should also push a "redirect-gateway def1" option so that all traffic (including DNS queries) goes through the VPN.
- Tunnelblick will set (temporarily, for the duration of the VPN connection) the Mac's DNS server to the address(es) "pushed" by the VPN server.
- That DNS server will be used for all DNS queries instead of the ISP's DNS server, until the connection is terminated.
If the DNS server does not "push" the "redirect-gateway def1", you can just include it anywhere in your client configuration file.
If the VPN server does not "push" its own DNS server to the client (your Mac), you would have to create a customized "up" and "down" scripts for OpenVPN.
Most VPN service providers do "push" DNS settings and "redirect-gateway def1".