Not only is there no reason it won't work, there is not much likelihood you will have any more buzzes or rattles versus not putting it in the cabinet two feet away.

The key however, is to cut out the bottom of the cabinet (as you already plan on doing), or you will establish a very boomy resonance with the cabinet. You will be just fine. We place subwoofers inside of cabinets in multi-purpose rooms ALL the time.