I'm replying to my own post because my Office 2013 has just updated to the latest level, three days after installation. I just wish Microsoft would publish more information about what to expect regarding the timing of updates. As my Office 2013 was only at RTM level just after installation, I was expecting an update to the latest level to happen fairly quickly. But it didn't.

To answer one of my questions. No, you don't have to be signed in to receive updates. But if anyone can give me a good reason why I should sign in, I will consider it.

I would still like to know whether I need to sign in in order to get a choice of Office backgrounds.