Two great questions!
First, let's cover a few basics: "power" = Force x Distance/Time. A good example of this would be an Olympic style lifter. They are the true "Powerlifters" as they utilize speed and strength to a much larger degree than what we like to call Powerlifters.
The point is, "power" is expressed by the work achieved in a unit of time, so it's obviously a combination of strength and speed. Therefore, the answer to your first question is a resounding no! As "pure power" is in fact the combination of both speed and strength. In short, you need to exert a greater force through a greater range of motion, in the shortest amount of time! This helps build momentum, which is essential to building that one set max reps that we all desire.
As to your second question: There is far to much general hype surrounding neurological efficiency. this is where I have alienated some people on this forum, as those individuals are afraid to look beyond the latest "hot fad" in the training world.
Neurological efficiency is one component to be sure. However, it should be relegated to the lower end of the spectrum as it is easily obtained through normal training routines, over a relativily short period of time. All of this talk about "greasing the groove" is utter nonesense (as I make more enemys).
Most who claim success using GTG are: 1. New trainees, who will succeed doing almost anything. 2. Regaining prior performance, "muscle memory." 3. Finally, being consistent in their training. As it takes consistency to perform x amount of reps throughout the day. And this while inferior to almost any other training method is in fact better than no method at all.
The truth is that many fail using this method! Those who fail using this method, and there are many of them, are found on various forums and gyms across the country. They are roundly chastised by the "herd" for not sticking with it long enough! If they object they are branded a "heretic" verbally beaten into silence and the charade continues! the lucky ones are simply told "well I gues this training method is just not for you." What a ruse!
Neurological efficiency does become important when you are learning a new motion, or are attempting to perfect a complicated motion, as you need to create efficient pathways. Some examples where neurological efficiency would be useful: Tennis, Golf, Bowling and even Olympic weightlifting! (one reason that the GTG crowd incorrectly points to Olympic lifters "the Bulgarians train three times per day so I have to do it to improve my Pull-ups"), to name just a few.
Why are these more complicated? When eyes, ears or feet are all being used to a more or lesser degree, newer and better neuro pathways need to be established. Now, please compare for a moment the basic dead hang Pull-up with my examples. The amount of new neurological pathways that need to be developed in order to efficiently perform a Pull-up, even for a novice trainee, can be developed very quickly in the course of more traditional training patterns. It is, in short, almost an unimportant detail!
Again, I am sure I have offended more people with the truth. I will not apologize for this. I am sure that some of those people were the same ones who ate the high carb, extremely low fat diets of the 80's and 90's.
I hope that this answers your two questions to your satisfaction. And thanks for asking!