Here's what I did, now have Notebooks synchronized between my Windows laptop at home, my tablet, and my work Ubuntu. It's not SkyDrive sync, but it works nonetheless.
I use a cloud provider that has sync agents for all platforms (I use Dropbox, but I assume Copy, UbuntuOne, etc. would work just as well). Install the agent to synchronize folders. I do NOT use the native Windows Live / SkyDrive sync in OneNote.
On your Windows machine, move the destination of the synchronization to a folder within the dropbox folder. Once there, any changes are synced immediately (so long as you have an internet connection).
On your Linux machine, open OneNote and open the notebooks directly from your synced dropbox folder.
Works well enough, you can even have the note open on multiple devices and they will update dynamically.