Dear Michael,
I just quickly tested on my iOS device by pushing the restriction policy to disable the App Store. Once the App Store is disabled through Afaria, the icon is deleted on the device automatically and the App Store sits in settings->Restrictions in disabled mode.
Well for the iOS devices if the App Store or iTunes Store is disabled, the apps DO NOT receive any updates on the device. In order to get the updates back to the apps we should enable the App store again.
Hope this clears.
Cheers,
Sushmitha