YES, you can. I've used an Airport Express as a wireless adapter for my Xbox 360 for 5+ years now. Mine is set up in bridged mode, where it joins the wireless network provided by my Time Capsule and both extends the wireless signal as well as routing the network to it's ethernet port, which is connected to my Xbox.
It looks like this is also addressed/explained in the third question on this [http://support.apple.com/kb/HT1515?viewlocale=en_US&locale=en_US|Apple support page]