It is certainly possible for OneDrive to run on a server (I don't know the Windows version specifics) but the users will interact with the files with the limitations of an SMB file share.
The scnario would be that users' Drive X is mapped to the server OneDrive folder (or parent folder). Users would be accessing the files as if OneDrive didn't exist.
This is fine for a single user but all the cloud-based multi-user benefits are gone, specifically user version tracking.
I would opt for having OneDrive files on demand on each client computer as the sole user access method. ... and using SharePoint rather than OneDrive.
The SPOD client could run on the server as an access point for the files to be backed up with other server files.