Will the physical sound waves that I produce with my loud speakers cause Active Noise Control enabled headphones to "engage" with me? Could I adversarially engage with them at that point?
While the noise cancellation is active it will attempt to neutralize (destructively interfere with) sounds from the outside, including those generated by your speaker. You could indeed adversarially engage through something like a spontaneous phase shift (so the interference will become constructive, making the resulting signal louder) or generating a frequency the ANC can't compensate.