If it's connected wirelessly, yeah, you can use it as a wireless adapter.
(assuming you're on XP)
Start>Connect To>Show all connections>Set Up a Home or small office network>follow the instructions. When prompted, say "This computer connects directly to the internet. Other computers connect directly through this computer." Also, be sure to specify your internet source when it comes up.
Test the connection on your Xbox 360 (I assume you're hooking up with a Ethernet cable) to acquire the IP address then connect to Live.