I do not get notifications even when the mail app is running... I searched the Internet, many people have this problem. I think you're right, we have to wait for an update.
Also, there's no "Mail" in "background apps" :-(
BTW: Yes, you can reinstall "W10 apps" like Mail:
https://thomas.vanhoutte.be/miniblog/delete-windows-10-apps/
https://thomas.vanhoutte.be/miniblog/reinstall-default-build-in-windows-10-apps/
Have you tried this method?
I have the same problem. Mail does not show up in background apps. Neither does Weather.
This is very frustrating.
Edit: So despite not appearing in Background Apps, my Weather tile is now updating... Not sure what to make of this. **Did an OS Reset which might have made a difference.
I dont have any problems with mail and other app live tiles everything is working fine with my system...i updated using USB though then again made a clean install.