Must an admin theme be enabled to be used?
No, it's not needed to enable theme to use it as an admin theme. You only need to enable it if you want to alter it's settings, both the ones in "appearance" section, and blocks. Just go to http://example.org/admin/structure/block/list/seven and http://example.org/admin/structure/block/list/your-seven-subtheme and set up the blocks the way you want them, that's all.