The physics of noise cancelling headphones is that they cancel out low frequency noise a lot better than high frequency noise. A good demonstration of this is to put them on outside as a truck goes by on a road. Uphill, say, with its diesel engine working hard. You'll notice that the engine noise is reduced a lot, but you still hear the tire noise and overall air rush at almost its normal volume.
Thus, and alas, noise cancelling headphones aren't as effective on the high speed dental drill as we'd like. They do still help though, from both the ears being covered and the noise cancelling electronics. Over a long career they'd probably make a considerable difference.