When you save to OneDrive it actually saves to your OneDrive Folder on your disk and then this is synchronised. So the answer is yes - it does it automatically.
See this tutorial for the setting up OneDrive -
http://www.eightforums.com/tutorials/28148-onedrive-available-offline-online-windows-8-1-a.html.
If a file is "online only" it is not on your disk until you try to open it. If it is "available offline" then a copy is also kept on your disk. Assuming you have space I find it more convenient to have everything "available offline" and so on my disk.