At one of my first appointments at my speech therapist, they did something along these lines to demonstrate that I could be fluent. It was headphones and a mic. The device introduced a delay from what I said to the headphones. The delay was adjustable, but IIRC, the delay was very slight. Likely no more than a second. That small delay allowed me to speak without my stutter. Knowing that I could be fluent was a great boost to my attitude towards speech therapy. They only used that device that once. It wasn't a solution. It was a tool to demonstrate that my stuttering wasn't immutable.