Yes, it should.
If you did not tell that Shaw Rep that your desktop has a built-in WiFi adapter, they were advising you that using a CAT-5E or a CAT-6 (but not a CAT-5) Ethernet cable is necessary, because a CAT-5 cable is limited to 100 Mbit/second, but the Shaw modem/router is capable of at least 1000 Mbit/second.