in order to use GFWL/LIVE you must move the xlive dll out of the halo 2 installation folder.
then start the game, signin, update/whatever, use your gfwl access code that comes with the game or gfwl game from 2007 through 2010. (thank gfwl play anywhere for that.) then have fun, it is possible to earn achievements via LAN apparently.
then if you want to play with people online you must then move the xlive dll back into the halo 2 installation folder.