Can I use my Mac to re-create an inverted audio noise cancellation effect?
Audacity can do this as far as I know. There is a White Noise generator, and under the Effects menu there is a "Noise Removal" option. 

I don't know if you can do it in realtime, but you could make a short recording of the ambient noise, run the Noise Removal, figure out what got removed (subtract before and after), and then play that part but inverted. Maybe....