Speed endurance does compliment max speed, but speed endurance does not EFFECT max speed. Max Speed and Speed Endurance are two entirely different entities. As mentioned, speed endurance is the ability to sustain MaxV over a longer period of time. Max Speed, or MaxV, is just that—the maximum rate of speed in which you are able to travel.
Now, with all that being said, what you want to work on and when will determine how you develop your training regiment. Most training regiments start off the season developing acceleration, moving into MaxV and finishing the season off by working on Speed Endurance. In this case, the early part of the season, the part in which the athlete is the freshest, MaxV is developed and you go into the end of the season, or towards the more important meets developing speed endurance. With this training plan, the CNS gets saved when most important (speed endurance training is actually less CNS-intensive than MaxV training) and peak MaxV can be utilized.
Be advised, just because you focus more on speed endurance in the aforementioned training regiments, there is still at least 1 day a week spent sustaining MaxV training. Also be advised that meets are considered speed endurance days in a training regiment as well and should be taken into consideration when developing a training regiment.