Have you ever mistaken "color TV static" for a king penguin? If not, then your built in DNN does a good job of discriminating between them. There are optical illusions that mess with our visual system, of course. You could I guess do something like raise a brain in one environment with statistics different from the natural world and then ask how that affects discrimination. Is that what you're getting are with "a gradient ascent method"? Because AFAIK we also don't have any proof the brain uses a gradient ascent algorithm so I'm not sure why you'd ask an in silico brain to carry one out
Gradient ascent is what you use to find the image that tricks the DNN. If you could run repeated experiments on a brain in exactly the same state over and over then you could perform gradient ascent on a brain as well. Whether the result of that hypothetical would be static that tricks the brain is unknown, but I don't see any reason to assume one way or the other. An easier experiment to help the discussion would be to calculate the probability that a random image of static can fool a DNN, rather than a special designed image that appears like noise. If the probability is not vanishingly small then there is indeed something fundamentally different at a functional level between brains and DNN. If not then we have to work harder to answer that question.
How do you know you can't? No brain of any kind has been scanned and emulated to the point where you could try such a gradient-ascent method.