Hi Chris,
You can create a general user and only add the user to local group "Users" in PC/Laptop, and then deny group "Users" to create file or directory on local PC.
After you complete these settings ,use the general user as credential to log into local PC/Laptop, and then prefer to the link below to map SharePoint Online library to a network driver:http://support.microsoft.com/kb/2616712
The general user would only be able to save data in SharePoint Online library.
This is only workaround for your reference.
Thanks,
Jacky Ding