Now the WIN8 user will need to update the download application in the Windows store as well as through the App Store itself, but there are indications in the leaked version of Windows 8.1 that users can later get an application update through Windows Update.
In a previous Win8 release, a movie Moments video editing application appeared, and in subsequent build 9385, an automatic push update was obtained through Windows Update, rather than through the Windows Store. This seems to mean that Microsoft has already been able to update the system's own application with Windows Update.
This view is not yet certain, because movie moments itself is not downloaded from the Windows store, but is built directly into Win8.1, so it can only be updated by Windows Update.
But it wouldn't be surprising if Microsoft really decided to update it in such a way, because the desktop's built-in apps and security patches are updated by update, and Win8 apps are through app stores, so the fragmentation of the two systems is a bit complicated.
At the moment, even if Microsoft arranges update updates for WIN8 apps, it's probably limited to the built-in Microsoft apps, and other apps will still be updated through Windows Store.