yes if you have a password protected site you can allow adsense spidering in there.
1. Enter an authentication rule
Specify an authentication URL and a set of parameters that will allow Google’s web crawlers to access your content.
2. Verify your site ownership using Google Webmaster Tools
We will direct you to Google Webmaster Tools, where you can verify that you own the site by uploading a file to it or changing the META tag of a file.
3. View your improved ad targeting
When your authentication rule is verified, you should see better ad targeting on your pages. You can check the status of your authentication rules at any time.
screenshot : click to enlarge 🙂