The Shinydrive for Content Server solution is designed to handle file transactions (reads/writes). The core concept is to:
Use Shinydrive to open a file in Content Server.
The file is then downloaded and cached locally in the background.
The user edits their file locally.
The user saves their file locally.
The file is then uploaded as a new version to Content Server in the background.
In that workflow, there are only two network operations happening.
OneNote is very "chatty" and every single OneNote character write if used via Shinydrive/Content Server will cause the ENTIRE Note to be written to Content Server (so, if you type in a 50 character sentence, that would cause 50 file writes to Content Server). The same logic applies to database files. They are meant to be written to and read from constantly. For this reason, we do not recommend using OneNote or Database files with Shinydrive/Content Server.
Microsoft has a Best Practices article for OneNote syncing, they do not recommend using anything other than OneNote to sync. For more details, please check out the article from Microsoft OneNote syncing best practices.