No, that's a function of Windows Networking. If you have two active networks, Windows assumes that the wired network is better and uses it instead of the wireless one. The reboot should not be required, though. Once you disable a connection, the other should come onto play and work.
On the other hand, the Centralized backup should work over wireless as long as both computers are on the same network and both computers have the network identified as "Home or work" for File and Printer Sharing purposes. The problem that I see is that both connections are active and OneCare has an issue with two active network connections and will make both of them "Public" - effectively locking down the file and printer sharing features in a private network.
Can you simply disable the wireless connection before running the backup via the wired connection and then enable it again after the backup has completed and you've unplugged the CAT5 connection from both?
-steve
