Regarding the offline files in general:
The files and folders that you've marked as keep offline are located within an encrypted synchronization cache and can't be accessed outside of your bookmark.
In summary, you need an active connection to the bookmark to see the offline folders. That means that you have to connect to your server once while you have access to an active internet connection. If you don't disconnect the bookmark and the connection to the server isn't interrupted otherwise you can still access the files that are located within the local synchronization cache. As soon as you are connected to the internet again, all changes are transferred to the server in the background.
Regarding the command-line access:
You can access the files and folders within the mounted drive with the command line (e.g. Terminal.app) as you would access any other files on your system.
Mountain Duck mounts your bookmarks per default in ~/Library/Group Containers/G69SCX94XU.duck/Library/Application Support/duck/Volumes but you can change the mount point to any other writable folder within the Mountain Duck preferences Connection tab. Note that you can't set the mount location to /Volumes if you are using macOS 10.14 or later where the directory isn't writable.