Snarky retort: Why would you buy a wireless internet stick if your router isn't set up for wireless connectivity????
Tech answer: This stick is only for wireless connectivity, and you must have a generated wifi signal for a connection to be made. If your personal router is not generating a wifi signal, then this stick will not connect to your personal router. However, it may pick up other random, close-by, or permanent wireless connection nodes.
Snarky answer: Yes it will when you reconfigure your router to generate a wifi signal.