The first person who hits the defined sever will seed the cache. The second and subsequent user will be pulling the cached items from the caching proxy instead of going out across your intranet to hit the Wiki. This should also speed up the Wiki for other users due to the reduced load.
What also should happen in tandem is the administrators of the wiki server should be setting policies on the server which allow for the caching of static content at remote hosts. If this happens then the only policy for caching which would need to be set on Squid or Varnish would be that of hosts, as the caching policy for the server could then be respected.