Zambonni, I don't think your method would work. The access point has to work by assigning an IP address to the linked network nodes (such as a USB wireless adapter). But what you describe is the reverse, with the access point pulling (instead of "pushing") the IP address, which is then translated through NAT to the Internet.
It seems like this would be easy enough to configure, and in fact it is, but what you need is called a wireless bridge, and these are unfortunately higher in price (~$70 and up) at the moment. For a wireless game system hookup, the wireless bridge in turn must be connected to a wireless router or a wireless access point connected to a router (and the router connected to broadband).
Wait a few months, and wireless bridges will get down to this $30 or $40 pricepoint.
If there were another cheap "hot deal" way around this, people would have found it long ago.