Yes, I learned to touch-type, and I would say it has contributed to my life enormously.
Prior to learning to touch-type I was a hunt-and-peck typist, like everyone else. If you watch a self-taught typist they get really good at hunt-and-peck - the hunt part gets really quick. However, virtually all of us who type like that have to shift our eyes between keyboard and screen. We've all glanced at the screen to see that we've been typing in all uppercase, for example. But this is the crux: self-taught typing is TIRING. There is no doubt that the up-and-down eye movements, combined with the ungainly hand movements (usually with no more than two fingers per hand), require a significant amount of brain power.
And this is where touch-typing comes in. You never look at the keyboard; you look only at the screen. In fact, you can happily look at the wall, a colleague, or another document. And you use all eight fingers plus (usually) one thumb, so the individual finger movements are much smaller, which is both more restful and faster. The reduction in brain workload is very substantial.
I never bothered to get fast: my touch-typing speed is 60 wpm at best, which is about as fast as I can think (really it's only copy typists that need to push the speed really high). But the best thing is: I can keep up 60 wpm for hours. Yes, literally hours. In practice, because I tend to spend a lot of time thinking, I actually expect to produce 1000 words per hour, and those words will have had the first pass edit (spelling, grammar) done on them. And here is the crux: it's not just banging out a thousand words in an hour: it's four thousand words in four hours. It is scalable.
It is made possible by touch-typing. Unlike the unstructured typing everybody does if they are self-taught, touch-typing happens at an unconscious level, and as such has practically zero load on your cognition. I literally cannot tell you where the keys are on a keyboard, but place my fingers in the proper touch-typing position, and I can just hammer out any word that comes into my head without even thinking about my fingers or the keyboard. It really is wonderful.
So touch-typing has made a massive contribution to my productivity. I know that my university results were boosted a lot by my ability to turn out plenty of work with little fatigue. And when I worked at BT's R&D place I could turn out substantial reports quickly and easily. Touch-typing has stood me in very good stead.
In conclusion, learning to touch-type was tedious and boring, and seemed to take far too long. But it is one of the best things I've ever done.