Lionel Logue: I believe sucking smoke into your lungs will kill you.
King George VI: My physicians say it relaxes the throat.
Lionel Logue: They're idiots.
King George VI: They've all been knighted.
Lionel Logue: Makes it official then.
King Edward VIII: Sorry, I've been terribly busy.
King George VI: Doing what?
King Edward VIII: Kinging.
Lionel Logue: Do you know the "f" word?
King George VI: Ffff... Fornication?
King George VI: If I am King, where is my power? Can I declare war? Form a government? Levy a tax? No! And yet I am the seat of all authority because they think that when I speak, I speak for them.
[watching a clip of Hitler speaking.]
Lilibet: What's he saying?
King George VI: I don't know but... He seems to be saying it rather well.
Lionel Logue: Do you know any jokes?
King George VI: ...Timing isn't my strong suit.
Lionel Logue: What was your earliest memory?
King George VI: I'm not...here to discuss...personal matters.
Lionel Logue: Why are you here then?
King George VI: Because I bloody well stammer!
Answer: The technique is called "masking" and all though it can sometimes help those who stutter it is not 100% reliable. It will make some stutter less, others will not notice any difference. It would probably be very inconvenient to Bertie not to hear himself at all during an important speech, not to mention that those around him might find the whole thing strange. You can read more about research on this technique and other similar ones here: http://ajslp.asha.org/cgi/content/abstract/16/1/77.
littlestar