As of Odoo.sh v.16.0 there does appear to be both a manual backup (in the shell) and a manual restore (in the Builds app).  

I have not tested it, but it appears to be a current feature.

Please, advise if I am incorrect, but it appears that I might be able to do a .zip backup from odoo.sh for offsite storage and then restore using the odoo-shell.

Hi Ray,

You can't restore a Odoo V10 or V11 database instance to Odoo.sh
The database manager is not exposed and it is technically not allowed by Odoo at this point - I've confirmed this with Jérémy and Martin from Odoo.
As Odoo.sh is still in beta all these features are not yet available. The platform is only for testing at this point. However, when Odoo.sh comes out of beta these features should be added (eventually). There is no time table at this period though!

Regards,
Yenthe