Yes. However, you must make sure that the version of Halo 2 you are trying to play is the PC edition rather than the XBOX version. It should read "Halo 2 for Vista" or something similar. Now this...
well, at halo maps.org you can get halo custom edition for free. it's the same thing, but without campaign mode. if that bothers you, then download a campaign pack for hce. i have the cmt halo 3...