If you use a generic USB wireless game adapter or Ethernet-to-wireless bridge, then you can swap the adapter between your Xbox and computer with no problem.
Using the Xbox 360 Wireless Networking Adapter
The Xbox 360 Wireless Networking Adapter is compatible with the original Xbox 360 console and the Xbox 360 S console. When you connect the adapter to the Xbox 360 S console, it disables the wireless N feature in the console. You might want to override the console’s built-in wireless functionality if your access point is located at a distance from the console. The external adapter can improve signal strength and bandwidth.
Common Xbox 360 Wireless Networking Problems
If you encounter networking problems with the Xbox 360, check these possible causes:
Xbox is too far away from the router, or too many walls and furniture are between it and the router. Move the Xbox closer to the router.When the Wi-Fi security settings are mismatched, the wireless connection on the Xbox will refuse to accept the Wi-Fi password. Check that the passwords are identical, paying attention to the fact that they are case sensitive.Other wireless devices are also running on the network and causing interference. Combat this by changing the Wi-Fi channel number or by relocating wireless equipment farther from the console.