I haven't read any of their dozens of book in their entirety. I assume they deal with Godel's theorem somewhere, but I don't know what they say about it. It seems like they do want to say not just that we know reality is mathematical, but that because that's so, we can know reality in a complete way. Then again, it doesn't seem like they accept all of math or even all of logic. They cherry-pick the parts that suit them.
They don't quite say the principle of sufficient reason is all there is to reason, since they add Occam's razor. Maybe they could exclude a void on the grounds of simplifying their ontology.
Again, I was only interested in this "Illuminism" as an opportunity to get clearer about the nature of mathematics.