I did some searching and the answer I found was "Yes, but you can't customize the controls", which sucks because I like using the left stick to accelerate / brake and the right stick to steer.
Of course, you'll still need the microsoft driver for the xbox controller to use it at all on your computer (assuming it's not already included with windows 7), but I assume you already know that.
Note: I don't own Flatout 2 or Windows 7, so I can't personally test this. I'm just parroting what I found on other sites.
Thanks for the info! Do you know if the Right Trigger is used for acceleration and if the Left Trigger is used for the brake?