I am pretty sure you are safe. As far as I can tell, the only time the check is done for new firmware is when a full sync is done. You can use the browser or the shop without it happening.
If it does happen, you will be prompted whether to apply the update. Answer no or cancel and then connect to you computer. You can delete the update files from the device. You can also do this if the desktop app does the upgrade. It simply downloads the files and copies them to the device. The update is not applied until you disconnect.
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