For the initial unlock, yes, your user will need to be online. This is due to the fact that the secured document needs to communicate with the Vitrium server (or your server if you install our software) to authenticate the user.
You can set up a specified period of “offline access” for your users but this would only take effect after the initial unlock. After this period expires, your user will get prompted to reconnect to the internet to re-authenticate and unlock the document.
There is an option in Vitrium Security that can allow users to unlock without requiring an Internet Connection (for the secured PDF file only, not the web document). There is an "Unlock Code" feature is available in the Vitrium administrative interface but this requires the user to contact your team to get access to that code.