Yep, any client without access to a particular Cloud drives API would have to use some other method. It should be the same as the GDrive method, just substitute that drive's sync folder for your chosen cloud drive client. Provided ALL your computers / devices can access the drive it should work.
Since I wrote this I've had a few disastrously failures using File Sync over a cloud drive. I got fouled up syncs a few times. So, I begrudgingly switched to using OneDrive for direct sync and have not had an issue with it since. It chaps my XXX to use OneDrive, I am loathe to use OneDrive but it works. I have few enough notes that it does not even come close to touching the limit of the free account. I am waiting for MS to screw this up or drop the free accounts. After that I think I will switch to manually syncing. This too is not available to Linux as AFAIK, MS never opened OneDrive up toe Linux clients.