I don't think you'd get the results you desire. To cancel the sound that you hear you'd have to grab the sound that is actually hitting your ear. If you playback the inverse of any other sound there is a chance ( I think a guarantee? ) that it will cancel some sounds but you will hear all of the other sounds that you aren't hearing that it is trying to cancel. I think that will just amplify the problem.

In other words : The recorded sound of the tires from the wheel well will differ from the sound that you hear in the driver's seat. You won't be canceling the sound you hear.