This morning i have received an email from Craig who has suggested a very simple solution to enable proxy in GO Contact Sync. The trick is to created a config file GOContactSync.exe.config in installation directory and put this content in:

<?xml version="1.0" encoding="utf-8" ?>
<configuration>
  <system.net>
    <defaultProxy enabled="true" 
                  useDefaultCredentials="true">
      <proxy bypassonlocal="true" 
             proxyaddress="http://proxy:80/" />
    </defaultProxy>
  </system.net>
</configuration>

Then replace "http://proxy:80/" with your proxy address. That's it.

Thanks, Craig!