[kevingadd]

Bluetooth audio introduces obscene amounts of latency. Whatever that dongle's doing, it's not broadcasting noise-cancelled audio over bluetooth. It's probably something low-latency like RF.

The wireless speakers/headphones and mics supported by typical mobile phones are all bluetooth. As a result, you wouldn't be able to easily (if at all) do noise cancellation for those devices via software.

You could totally do it for wired headphones, though, if you sorted out the mic positioning problem and the processing latency problem! The processing latency issue is the big one, in my opinion. Doing it without dedicated circuitry on your iPhone without the interference of other (system or user-mode) software is gonna be tricky. A pause on the order of 3ms could be big enough to cause audible glitches in the noise cancellation or give you a headache.