I'd say no.
The strength of Sid's wall and the beauty of In Tent's walls were the things they were optimizing for. See: http://lesswrong.com/lw/tx/optimization/
The height and beauty of Sid's wall were side effects. They were not what he was optimizing for, but they were consequences of the actions he took to maximize strength, and he may or may not have been aware of them.
The strength and height of In Tent's wall might be labeled side effects, but I think a distinction should be made because they were specifically chosen. Where Sid's wall became beautiful haphazardly, he had no bias in either direction, nor a bias towards 'reasonably tall'. In Tent's wall grew tall in a precisely chosen way. Every inch of height was required to maximize beauty. (And if he had not been strictly maximizing beauty, he could have chosen any other balance.)
I don't think an In-Tent-style no-side effects model is possible outside of mathematical systems like certain puzzles or programs.
And of course evolution doesn't intend anything, so you could say all the design was a side effect of the process, or that 'side effect' doesn't apply because there was no goal.
But I'm looking for a more technically explicit definition so we could look at the process leading up to a specific 'design choice' and say it has an intentionality of .0002 or .96.
But I don't think I gave good examples of processes with moderate levels of intentionality. this story was very either-or. A spectrum of genetic algorithms might do the trick.
Three different Martians built the Three Sacred Stone Walls of Mars according to the Three Virtues of walls:Height, Strength, and Beauty.
An evil Martian named Ution was the first and stupidest of all wallbuilders. He was too stupid to truly understand even the most basic virtue of height, and too evil to care for any other virtue. None the less, something about tall walls caused Evil Ution to build more tall walls, sometimes one on top of the other.
At times his walls would fall as he was building them, he did not understand why, nor did he care. He simply copied the high walls he had already built, whichever were still standing. His wall did achieve some strength and beauty. Most consisted of thousands of similar archways stacked on top of each other. Thousands upon thousands of intricately interlocking stones. Each arch a distantly removed copy of some prototypical archway that was strong and light enough to support itself many times over.
To this day his walls are the highest in all of Mars.
Many Martian Millenia later came the next great wallbuilder: Sid.
Sid was far more intelligent than Ution, but he was just as single minded. We know from his archived odor sequence deposits that he understood the virtues of height and beauty, but celebrated his own willingness to sacrifice them entirely for the tiniest bit of added strength. When a critic asked why he did not simply place a one solid ugly stone on the ground, he replied simply "Fool! A single stone can yet be moved."
Indeed, Sid's walls are shown by modern computer modeling to be stronger than any solid stone available on Mars at the time. The intricate interlocking matrices of cut stone redistribute stress so well, and the wall are so tightly anchored to the bedrock, that an underlying fault line has been repaired. This causes tectonic stresses even in far distant parts of our planet.
Despite the fact that Sid clearly made every decision exclusively favoring strength, his walls also hold the virtue of beauty and height. While some of these virtues he knowingly permitted as they did not detract from strength, others were hidden and not discovered until after the wall was built. In one particularly delightful section of his wall hundreds of tall cylindrical pillars stretch out in a line. Tourists have learned that by slapping your tentacles together in nearby areas you can hear a delightful chirping echo as the sound bounces off each pillar in turn.
In his honor, this beautiful phenomena has been termed the Sid Effect.
But the most beautiful stone wall was built as an engagement gift. Though his name was lost to history, we know he was too poor to own a proper house, and needed an impressive achievement to impress his bride. His identity was recorded only by his dwelling: "In Tent".
As the legend tells it: This young Martian set out to build the most beautiful stone wall possible. Common wisdom at the time held that beauty was merely a label assigned to things by the Martian brain, not a real attribute of objects. He was the first to realize that you could still treat it as a measurable quantity and if desired, maximize it.
His first wall was merely the basis for a few simple empirical experiments. Based on his collected data he took months creating a theory of beauty while spending his evenings hiding outside of his beloved's chamber and injecting other would-be suitors with dihydrogen monoxide, thus rendering them incoherent and unattractive.
He was well aware that a some amount of height and strength were fundamental to any wall, and these actually became parameters in his model so that every stone laid served each purpose in a precisely chosen way, and even this attention added to the overall beauty. Thus he crafted the most beautiful wall possible that was both reasonably tall and strong enough to be a symbol of lasting love.
Upon it's completion he burned his notes and presented the wall to the Martian who would become his spouse.
As you can see, each of the virtues can come about by any of: a practically mindless churning, being an incidental consequence of some other plan, or through a known and chosen perfect beautiful design. Yet in each wall we can see not only the primary virtues which drove the builders, but also how they thought of each virtue (if at all). Using our modern theory of wallbuilding (and wallbuilders) every feature speaks a little something about what (if anything) the builder was trying to do.