No, because active noise cancellation doesn't offer any hearing protection. It doesn't make the noise go away, it works by sending out an extra soundwave which is a mirror inversion of noise to be cancelled, sends out peaks where there were troughs and troughs where there were peaks, and they cancel each other out as far as your brain is concerned. But to work the destructive soundwave has to be as loud as the sound it's cancelling, and now you have two sound waves blasting away, still moving air and putting pressure on your eardrums, and it's that pressure causes the damage to your hearing.

Proper PPE has a passive barrier that physically blocks the bulk of the vibration from reaching your eardrums in the first place. Active noise cancellation does kind of the opposite of that.