Every hotel Ive ever been in (and Ive been in a LOT of hotels) the first time you connect, you have to accept their agreement on a web page. From there on out, that port in the room is tied to the MAC address of the machine you connected with. I dont see how you could get past the initial web page from an Xbox.
You could possibly try a router...that way you could hook a computer up to it to accept the agreement and then it wouldnt matter what you hooked up to the router because the MAC wont change. Most routers will also allow you do spoof a MAC, so you could hook up the computer, log onto the web page, and then spoof the computers MAC on the router and teh hotels ISP is none the wiser.