So, to answer the OP's question... Yes, complexity has worked for me as a DM.
In general I make work by cheating with smoke and mirrors. Let me exaplain...
I don't often have time to fully develop an adventure on my own, so usually my first step is to find a published adventure to use as a basic framework. From there, I build simple goals and simple connections between the major players in the addventure. To use my current adventure,
Dark Harbor, as an example:
The Celtiberians: The recently united Celtiberian clans want to take advantage of the wealth of Tartessos. They would rather draft a treaty that accomplishes this and places Tartessos under the control of King Arganthonios, but will invade, if necessary. Lord Juthe has been sent to Tartessos to negotiate the treaty on the behalf of Celtiberia.
The Aristicians: The faction of the Tartessian City Council that welcomes a treaty with Celtiberia. They see it as a way to acquire the wealth, power and military might of the barbarian kingdoms from within, and also as a way to avoid a costly war.
The Mariners: The faction that opposes a treaty with Celtiberia. They would rather keep the wealth and power of Tartessos to themselves, and don't believe the barbarian army to be a signification threat to the city.
The Via Sanguinaria: A reckless death cult that seeks to incite rebellion within the the city slums and overthrow the City Council.
And so on...
Now here's where the cheating comes in... I tend to keep the major plots point simple and fairly straight forward. I add in little details that fill in the gaps, and I feedback any little musings and discussions the players have within my earshot. These details don't appreciably affect the complexity of the major plots, but give the
appearance of complexity.
My other trick is to plan far ahead for the bigger plot points, but only in a simple, vague way -- flexibility is the key when you plan that far ahead. That way I can add in little foreshadowing hints early on that let the players say, "Aha!" much later. Again, this gives an illusion of complexity without necessarily complicating the plot.
For example, a magic book about summoning demons was purchased by the leader fo the Via Sanguinaria. The book was recovered, but the leader escaped and was obviously taking notes. This will resurface as a hook and a major plot development for a later adventure.
Or, the players discovered the cryptic last page of a blood-spattered letter written by "V. Servius Strado". It has practically nothing to do with the current adventure, but will be a obscure tie-in to
Expedition to Castle Ravenloft, which I plan on running sometime in the future in the Victorian Age version of the same setting.
For actual complications, I can usually leave that to my players... Whenever they do something a little unexpected I simply ask myself, WWTBGD? A adjust the adventure accordingly, and plot twists naturally ensue.
For example, during their search for the magic book of summoning demons, the players spoke to a local herbalist who was rumored to be a magician as well to see if he had any leads on it. This herbalist is also a poisoner behind the scenes, an actual wizard (which are exceptionally rare in Iron Heroes), and a rather shifty fellow on top of it. He agrees to make his own investigations (which he will), and also to pass along any info to the PCs (which is a blatant lie). And now there's a third party looking to acquire the book for his own purposes (which I haven't detailed just yet).