In order to produce a significant advantage in combat as a result of faster reaction times, it is necessary to either operate inside of the opponent's decision/action loop (i.e achieve tactical surprise), thus requiring the opponent to think about reacting to a situation that you have already thought about, or to significantly decrease the opponent's physiological reaction time. Cutting a few percent off the reaction time won't be sufficient, you'd need to have a quite significant reduction in reaction time to observe any significant combat advantage. We're looking at about a 15-20% reduction in reaction time at minimum.
If you had no limits as to the sophistication of your genetic engineering other than the practical limits of the materials you're working with, have a look at my answer to the second question referenced. To summarise, neural conduction could be accelerated by precipitating metals (or graphene) and neural connections could be accelerated by using mechanical rather than neurotransmitter-mediated gates.
It would be rather more difficult, but not impossible, to dramatically improve the speed of muscle contraction, but by dramatically reducing reaction times at least, it would be possible for a human so enhanced to out-think and out-react any unenhanced human, with or without higher muscle contraction speeds.
Human eyes are not the fastest eyes in the animal kingdom either, so it would not be too difficult to make the necessary changes to speed them up either.
Given all these advantages engineered into a single individual, including faster musculature, it would be possible to see bullets in flight and to have a chance to dodge or deflect them, though the chances would probably be on the order of an unenhanced human dodging or deflecting an arrow from a bow - very difficult, but not impossible at sufficient range.
If it came to combat of any sort between enhanced and unenhanced humans, the outcome would be heavily skewed in favour of the enhanced human, regardless of the training of the unenhanced human and any lack of training of the enhanced human. Unenhanced humans would have to rely on attacking unobserved or using heavy weaponry to have any certainty of defeating such an opponent.
However, this would come with certain disadvantages.
Unless the genetic engineering was done very carefully and cleverly, such a 'human' would not actually be human in anything but appearance. The most likely outcome is that they would not be sufficiently genetically human to be able to successfully interbreed with unenhanced humans, and even in the unlikely event that they could, their offspring would be far closer to the unenhanced parent than the enhanced parent.
Secondly, during pregnancy and childhood, if metal precipitation was used to accelerate axonal pulse transmission, it would be necessary to supplement the diet with the metal in question, probably silver due to its low resistance, as the levels of metal required would not naturally occur in an unenhanced human's diet. However, graphene precipitation would not have this drawback.
Thirdly, as speed increases, so too do metabolic costs. Enhanced humans would have a higher basal metabolism simply due to their more active neurology, and acting more rapidly would have a similarly higher metabolic cost. Put simply, these people would have to regularly eat the sorts of meals that for the most part only morbidly obese unenhanced humans would choose to eat.
Fourthly, were such enhanced humans engineered, and they constituted a separate species as is most likely (and even if not), there would be a strong impetus for active competition between the groups to occur, as slower or not, unenhanced humans are still smart and quick enough to see how they are outclassed. This could quite quickly descend into a war between the enhanced minority and the unenhanced majority a-la the Marvel X-Men universe.
Fifthly, enhanced humans would not obtain the same enjoyment from the movies that unenhanced humans watch without software enhancement: since we are talking about enhanced humans having faster eyes, this would increase the fusion frequency. Our movies are typically shot at around 25 Frames Per Second (FPS). However, this would be below the fusion frequency of enhanced humans, who would see a series of static images. Enhanced humans may have a fusion frequency requiring frame rates of 50-100 FPS or even more. This may be able to be compensated for by inter-frame interpolation, but would require a lot of computing power.
From an evolutionary perspective, it would be very difficult to evolve these adaptations, even in the presence of an evolutionary stimulus. Sodium-gate neurotransmission is so heavily tied into the viability of organisms that any mutations which affect this would be highly likely to result in a non- or less- viable organism. Evolution is far more likely to produce iterative improvements on the current theme, not a wholesale cut and replace solution such as the genegineered solution above. Creatures have been evolving side-by-side for millions of years in an attempt to out-react one another, and the current neurology is the best that has occurred naturally. Any significant improvements would have to come as a series of individually viable steps, each of which provided some advantage, whereas geneginering can implement a whole lot of steps at once without requiring incremental advantage.
Evolution is limited in that in a solution space with multiple uneven peaks, solutions will tend to move up the current gradient to the top of the closest peak, and to jump across to an adjacent, higher peak is effectively impossible, as this would involve a reduction in fitness before there could be an effective improvement in fitness.
This means that when starting from a different evolutionary point, it might be quite easy to evolve a faster system such as this, but we can't get there from here, since we can't go backwards.
From a certain point of view, genegineering is an evolutionarily valid solution to this problem: your species, (humans in this instance) have evolved high intelligence, and have used that to accumulate a cultural store of knowledge which can be used to develop techniques of genetic engineering, hence it can be said that humans are in the process of evolving the ability to produce game-changing advantages in future generations in a very short timespan. By evolving high intelligence, we are in the process of gaining the ability to potentially jump to an adjacent, higher peak of fitness without the necessity to suffer generations of lower fitness first. Why say that evolution always has to be unintelligent? We're becoming quite capable of our own intelligent design, no prehistoric creator needed.