Yes, it is possible to add links to local files/folders on start.me. You'll need to have the latest version of our Chrome version installed for these links to work.
You can add these links to a regular bookmark widget.
Format of links:
file:///d|/testfolder/test.txt (links to a file named 'test.txt' in a folder named 'testfolder' on your D-drive).
You can also add links to chrome internals, like: