Although this will work, I think you are going to be more than dissapointed with the results, especially if playing games. Remote Desktop is meant to be used as a server tool or remote help system. You will get frame rates around 10 at 640x480. Basically, you'll have better luck playing the games on your mac. Do yourself a favor and buy a good monitor, you can get them for under 200 now anyways.
BEN