If you check the Windows Task Scheduler under Mozilla, you will find a task that runs every 7 hours to check for updates in the background (at least this is the default configuration for the regular release; ESR may vary).

It has a lot of parameters I don't understand, and don't know whether they are unique to my installation, but at the end, this switch seems to be the important part:

--backgroundtask backgroundupdate

You could experiment. Or wait for someone with more information.

I've moved the thread to Firefox for Enterprise to see if Mike Kaply has some suggestions.