No. And that's what's so brilliant about it! I remember very clearly, in one of my Zoology lectures, now so long ago, our lecturer trying to hammer into us this simple fact. The focus of his statement was slightly different, I must admit. What he actually said, more than a few times over, is that a more complex species is not necessarily more highly evolved.
Let's start by looking at natural selection, the antagonist to evolution. A species has many traits, or characteristics, which make it well suited to its environment. Birds have fused bones to make them lighter for flying. Cheetahs' legs are extended from the heal leaving only the toes to touch the ground, thus extending their stride for speed. The blue whale has a 2 meter thick layer of fat surrounding its entire body to keep it warm in the coldest oceans!
When a species requires a certain trait in order to survive, animals with this trait are more likely to live to reproductive age and, therefore, more likely to pass on their genes. This perpetuates the necessary trait.
The most famous case for the process of natural selection (still under debate) was that of the Biston bitularia moths (Kettlewell, 1958). In England, before the industrial revolution, a typical population of these moths contained roughly 95% white moths and 5% black. The white moths were camouflaged against lichen clinging to the trees and so were hidden from potential predators.
However, the industrial revolution, with all its resulting pollution, caused the lichen to become covered in soot. Suddenly it was the black moths that were camouflaged against the dark trees. These moths, having a greater chance of survival were more likely to reproduce, passing on their black' genes. Soon the population statistics swung to about 95% black and 5% white. The black moths were no more complex in form than the white variety. They were simply better suited to their environment.
Evolution works in much the same way but over a long, long period of time. What's important is that it is not the more complicated characteristics of a species that survive but those best suited to the species needs. Once a species establishes a good relationship with its environment, with the ability to adapt to at least non-catastrophic changes, it could be considered well evolved'. Complexity doesn't necessarily come into it at all.
Insects are arguably the best evolved and by far the most successful group of animals on earth. They certainly seemed to forego the evolution into more complex forms. They must be content just to do what they do best and are rather good at it