Yes, the boot receiver is registered to listen to the download, so if you reboot your device, it will work, regardless of whether the application is running or not. Similarly, if you add NFC listeners to your manifest, then if someone checks the NFC card, the application will respond. The manifest is used by Android to respond to everything you specify in it. It does not depend on whether the application is running (or has ever been executed). Great question though! :)
EDIT according to other answers and documentation. This is no longer the case. Sorry for the confusion.
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