Not at all...
The increase of energy is (supposed to be) exactly the same amplitude and shape as the sound going into your ear, but with opposite polarity.
Sound is basically the air rushing forward and backward very often - what ANR does, is when the air molecules are rushing one direction, it adds energy in the OPPOSITE direction. If it gets it perfect, the air has the same amount of force pushing it forward as backward, so it doesnt move either direction.
Then you hear silence.
The technology isnt perfect, which is why you can still hear engine noise etc, and it works better with low frequency ranges than high, but thats the basic idea.