Well it must be up to the developer on where/how it stashes associated files?. As you can go looking with an explorer and see folders stashed away with files/settings that are retained/left behind from long gone apps.
I well aware of your clarification to the storage because 'the people demand'. Which is what made me think it was somewhat a over-look as a means to leave the data behind to manually check/keep once the push notification ability is gone should it be removed by user