Explore mode doesn't work out of the box with Crossover and I don't expect it to work any time soon with how it calls for an outside program to run.
Here is how you can get it to work though.
Step 1. Open Crossover > Programs > Run Command.
Step 2. Navigate to your Steamapps folder and the Natural Selection 2 game files.
Step 3. Run Server.exe (By default it will be a 4 player server in Explore mode. If you are trying to run an actual server, see Natural-Selection 2 forums and website for information on altering settings).
Step 4. Run Natural Selection 2
Step 5. Open console by using the ~ key and type "Connect localhost" (127.0.0.1 also works)
And Bingo your in, once you've joined it will spit out a bunch of text on admin commands and such, use those to change maps and settings within the explore mode server.
Explore mode is a great way to learn the maps and find those sneaky spots to hide yourself as a skulk or Lerk. Have Fun!