I don't know about that. I think it depends on how you count the complexity of a model. There's three cases: a) insects are less complex than machine learning models, b) both are equally complex, c) insects are simpler.
If (b) or (c) is the case then we're shafted, because we're failing to reproduce insect behaviour despite building systems at least as complex as theirs. If (c) is the case, we're particularly screwed because it means we're missing a simple, more efficient way to do things.
If (a) is the case then we may have a hope to get to where insects are in terms of complexity and possibly reproduce their behaviour. Still, there's the issue of combining models to perform well at a broad range of tasks, which is far from solved.
^ http://www.annualreviews.org/eprint/5PHddkgYYKaduPp4CcN5/ful...
Learning algorithms construct a model of data- that's what we call "learning", or "training". The trained model is then used to make decisions, so that's what you would deploy in a production system.
In that sense the deployed systems don't learn any further, yes, but that's because you don't deploy the algorithm per se.
An exception is what is known as "online learning" algorithms, that can continuously update their model as new data becomes available (hance, "online").
And, technically, the manner by which most nets are trained, via (minibatched) stochastic gradient descent is online. But the architectures are so ill-adapted to learning continuously and backprop is so data inefficient that retraining on new data is often just better done from scratch (or at best, freezing weights).
Of course spiders are complex. Everything in biology is complex. It's been slowly refined over millions and millions of years. Countless trillions of tweaks to its DNA tested and rejected until it hit upon something that worked. No human could design something as complex as a spider.
Our artificial neural networks are just as complex though. AlphaGo probably knows millions of facts and heuristics about Go. You would never be able to understand everything it knows. Even though we didn't create the complexity ourselves, we "evolve" it just like the spider, sometimes even with algorithms based on evolution. But we have much more efficient algorithms than that, like backprop.