Tunnelblick doesn't include this ability in the standard scripts it uses to manipulate DNS. So you would have to modify Tunnelblick's standard up and down scripts to accomplish this, or create your own scripts. (See
If you end up doing this, please share your scripts so they can be used by others. I'd love to put such a script in the User Contributions section of Tunnelblick's Downloads page, or better yet, incorporate the functionality into the standard scripts.
It's a bit complicated because on OS X, DNS is done very differently than it is on Windows. On OS X, the first nameserver is used until/unless it stops responding. Then the next one is used until it stops responding, and so on. There is a 30-second timeout before OS X decides that a nameserver has stopped responding, so this takes a long time. On Windows, all nameservers are queried at once, and the answer from the first to respond is used. So you can't just "add" the extra nameservers on OS X as you can on Windows; you have to set DNS up to use particular nameservers for specific domains.