The GPL doesn't propagate as long as you don't distribute the program. It doesn't have anything to do with using it like proprietary software. If somebody can download your program, you have to honor the GPL.
It isn't the source code redistribution or availability that is the problem with GPL on an app store.
You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form...
The app stores do not allow you to copy and distribute the Program in executable form, since they are wrapped up in DRM layers and I would bet there are also license verbiage that says you are not allowed to copy the apps downloaded from the app store. It is very easy to provide the distribution of source code for an app on the app store, you just point to a file on the internet, a phone number to call or an address to write to asking for the source.