MySQL doesn't support SSH. So there's no driver that does either. An ssh tunnel is a completely separate thing that only transports data packets from one machine to the other using encryption to secure the data in transit.
Depends on what the database owner wants and can support. In some cases we get a database dump which we retrieve with sftp. In other cases we use a site-to-site vpn.
If necessary you can also create an ssh tunnel over the vpn for an extra layer of encryption. But that's something you set up separately. Then you simply point the odbc driver to the right ip and port to establish a connection over the tunnel.