Sure, I would agree with that wording.

In the same way, neural networks which are trained to do a task could be said to be "designed" to do something.

In my view, there's a big difference in what the training data is for a neural network, and what the neural network is "designed" for.

We can train a network using word completion examples, with the intent of designing it for intelligence.

I could also argue that the word "design" has a connotation strictly opposing emergent behaviour like evolution, as in the intelligent design "theory". So not the best word to use perhaps.

And in your example, just because we made a system that exhibits emergent behaviour to some degree, we can't assume it can "design" intelligence the way evolution did, on a much, much shorter timeline, no less.