No. While it seems possible, at least for OneNote 2016 (Office version only), to save your locally stored notebooks to the sync folder of Dropbox or similar cloud services, this will lead to massive problems (sync errors, duplicate sections). The reason for this is that OneNote needs to use a special sync protocol (COBALT) to transfer only changes applied to single objects on OneNote pages instead of complete section files (what Dropbox or Google Drive are bascially doing). This protocol is not supported by other cloud services than OneDrive and OneDrive for Business (and Sharepoint by the way). More information about this in this article.