If your goal with the AirPort Express is to extend the wireless range of the Extreme then it suits this purpose well. Please check out the following AirPort Support article for details.
As far as Xbox gaming is concerned, the Xbox itself shouldn't have issues connecting to this extended network. However, it is important to understand that some bandwidth (speed) is lost due to the overhead of maintaining an extended network. If properly set up, your Xbox should not experience any significant loss of performance.