It could very well be shorthand. I just picked up my information about it from amazon.com, and it doesn't really go into detail about what "Talktation speedwriting technique" is.
If I'm at home, I'll type the paper to begin with. However, if I'm at school I'll begin writing by hand, and then copy that to a computer at home (computer lab at school is too distracting).
Anyways, I just thought it would be very useful to be able to finish a 1000-word essay when I only have a 1 hour break between classes.
As for how quickly do you start writing faster, It doesn't give those details, but I would assume that it's as soon as you start implementing it, since it doesn't seem like something that would take extensive practice.
If anyone wants to, you can check out this page on Amazon: