Here's the thing. Those wireless adaptors will still require an ethernet plug to actually stick into the console. You need the 'wired adaptor' to even use these wireless options, otherwise you won't be able to plug the wireless ones in.

As for your question, the speed of the device doesn't currently affect your internet speed much. Unless your internet connection is faster than 11Mbps (the 'speed limit' of the wireless routers), these won't slow it down.

FF11 isn't a game that requires high-speed internet to enjoy on a basic level. You can play it through dial-up as well... after you get the adaptor.