Does this Range Extender work with Xbox Live?

I am buying a Xbox 360 on Saturday. I got a range extender cuz my wireless router is 2 floors below my TV that I am going to plug the Xbox 360 into.
I have tested the connection, and the range extender does in fact bring up my connection to my highest floor.
But will it work with the Xbox 360?
Here is the link to the range extender:
http://www.amazon.com/Linksys-Wireless-G-Range-Expander-WRE54G/dp/B00021XIJW/ref=pd_bbs_2?ie=UTF8&s=electronics&qid=1195505275&sr=8-2
*Note my router is also a Linksys.

Range expanders are good, but I perfer adding an additonal wireless router to the network. Much more cost effective.

$50 opposed to $90 or what not