I've had people suggest you write long-hand first drafts because it makes you slow down and think about your writing. I don't know if that's a plus. I like writing long-hand because I don't always have a computer and/or it's faster to just pick up a pen and get to work. I don't like then having to type legal-pads-worth of writing into the computer. But I do touch-type.
If you're going to learn, perhaps using the non-QWERTY setting on your computer keyboard might increase your speed. There are various keyboards. I did a quick search and there are even some keyboards for hunt-and-peck people. Realize that the QWERTY keyboard wasn't designed ultimately for speed (most of us are right-handed but the major keys are in the left hand), but since most people learn to type that way, it's tough to switch.
That said, I couldn't imagine having to hunt-and-peck to actually capture a story I'm working on. I get frustrated enough with the mistakes I make as I touch-type.
As far as touchscreen technology, again if it's set up like QWERTY, I can't imagine it's going to make that much difference for speed, accuracy, or ultimate "text quality".