This would only work if the queuing system kept a constant, unique, audio link from you open at all times. Whilst this is technically possible, many IVR / Autoattentant systems simply connect you to a common audio source (music on hold, comfort messages), and don't bother listening to you unless they really have to.
The resources required for speech recognition are also pretty high, so it would need a pretty beefy system to be performing speech rec on every inbound channel 100% of the time. Usually these resources are only allocated when required, i.e. when you've been prompted to say something.
So whilst it might work on some queuing systems, and the idea that an Apple system would be "spying" on you all the time isn't exactly shocking to me, I wouldn't go banking on it working in every situation.
You'll probably have more luck having a keyboard mash (don't forget * and #) and finding a get out of jail that way.
Alternatively, and preferably, just spread the news of the terrible support far and wide. This will reduce the number of customers, and hopefully you position in future queues if you haven't seen the light and taken your business elsewhere.