Absolutely. Touch typing is a game changer, not only because with practice, you can just think the code and see it appear on screen, but because you no longer have to glance at the keyboard and your full attention is on the code.
If I'm creating something from scratch or refactoring then a keyboard definitely gets in the way. Of course when I'm writing something from scratch I usually iterate a few times before I have code that I'm satisfied with, so going through those iterations requires a lot of moving things around.
If I'm solving a hard problem (i.e. architecting a system or coming up with an algorithm) then 99% of my time is spent thinking rather than typing.
Not writing from scratch, and not what I consider "nice" code (specifically avoiding the term "good" here). There are plenty of cases that wind up being typing jobs essentially. Usually, that means you're not really designing code as you write, though.
Depending on what I'm working on, just dumping stuff to an IDE buffer at 70WPM can be 10% or more of the time something takes. Which is enough that typing slower would have a noticeable impact.
Typing hardly registers as a factor when it comes to how long it takes for me to code anything, at least.