No. The wireless adapter will only work with a router which broadcasts a signal, not a wired router.
As for internet sharing, yes, that will work. It will take some patience to get it working. In Windows 7 or 8, go to the Start Menu and type in "Internet Sharing."
Once the setting is enabled on your LAN Ethernet Adapter, you'll be set. What you'll need to do now is have an Ethernet cable ready and connect it from your Ethernet port on your laptop to your Xbox, and test the connection.
If you have other issues, let me know. Sometimes Xbox will ask for some ports to be opened. If this is the case, a quick Google search will help.