Short answer: Yes.
Disconnect the cable modem from the PC and turn it off for a minute (may have to unplug it). Connect the provided ethernet cable from the cable modem to the Internet slot in the new wireless adapter and plug the wireless adapter's power in (and turn it on, if there's a switch). Turn the cable modem back on. Give the devices a minute to talk to each other, then you should be able to configure your dlink router at http://192.168.0.1 There is typically no default admin password, though you should set one.
If you don't change it (I would suggest that you do, actually), the wireless network will be called "dlink". Plug an ethernet cable from the outbound slots (often numbered) of the adapter to any wired network devices if you feel like it. You should now be able to connect to the wireless without having a desktop plugged in.