From wireless to ethernet. Will this work?

I have a desktop computer that is on my wireless network at home. I want to set it up in the basement where the signal is weak, so I bought your USB 2.0 Ethernet Adapter 10/100 Mbps. Can I install it in the computer without removing the wireless card? And, if I can, will it then connect to my Time-Warner router via ethernet cable(it has an ethernet plug on the back) ? And, will the computer have any trouble getting internet then?