Not on mine. If you are logged in with youre MS account click on the icon to the left of the search bar in the Store app and check for updates. It is not doing it through the normal update process.
Store Auto Updating can be turned off but AFAIK it's on by default.
I have battery saver mode enabled and it will not download Windows Updates with battery saver on however that doesnt seem to stop the Store from updating apps. In App History (Task Manager) Store is my number one Network user. Although for some reason (probably because it's deprecated) IE doesnt show up in that list and I'm using IE exclusively so there should be plenty activity to a least post a number
There must be a setting on my system that prevents it from being automatic, otherwise there wouldn't be 16 there when I check and I check for the other updates at least once a day.