Piwik can track visits on your intranet website as long as Piwik itself is hosted in your intranet. To make sure that all unique visitors are tracked correctly in your intranet, please edit your config/config.ini.php and add the following:
[Tracker] trust_visitors_cookies = 1
This will ensure that even if all visitors have the same IP, browser configuration, OS, etc. they will be counted as unique visitors based on the first party cookies. If not set, you will see a lower number of visits.
If you track in your Piwik both intranet and internet websites, this setting will also apply to your non intranet websites. We plan to differentiate between Websites and Intranets in a future version (more info)