No. I don't. It's possible, but I've seen nothing to indicate that belief in Powers capable of thought we are intrinsically incapable of understanding, Power capable of "solving the First Cause", is anything more than religious faith.
Here's what "Perceptual Transcends" mean to me. There's a picture in _GEB_ of all truths (or theorems) and those which are recursively enumerable, if I remember my terms correctly. The former is a square containing the latter represented as a fractal tree. If that tree is all of human knowledge, everything we have learned through millenia of trial and error, and a newborn Power has every branch of that tree as an obvious primitive, it is still inside the square. It can more quickly explore several more fractal branch-layers of truth, but all those truths could well be still comprehensible to a broad-minded human with enough time and desire to learn.
The Enlightenment after Newton thought of the universe as a clock. More recently we thought of the universe as a computer -- but that's really a more complicated clock. Now we have quantum mechanics and the metaphor of cellular automata running around... but the universe still seems fairly conceivable as a complicated clock with dice in the spring. Perhaps those dice represent something fundamental we don't know... but perhaps not. Dice make at least as much sense as a clock.
And we -- or many of us -- seem to be universal Turing machines, or capable of acting that way. Given this view, it is hard to see how the universe could generate any problems not capable of being comprehended by us, apart from existence. There could be things our minds aren't big enough to grasp, ideas we don't have the memory to hold the parts of; there could be Powers capable of thinking faster than we do; but those are the differences between a computer with 16 megs of RAM and 4K, or between a Pentium and a 8086. A qualitative difference would be that between any computer and a wristwatch. To believe that there is such a difference above us is purely a matter of belief. Act on it if you wish; I find myself believing that no Power could do something which a liberal-minded cosmopolitan could not understand, given time and data.
My very vague thesis: All undamaged human beings, and other sentiences, share the same area of comprehensibility.
Corollary: "I" may never know if I'm wrong.