Would Schmidhuber's theories of everything be capable of performing hypercomputation?
If the hypothesis is that we live in a universe whose physics are computed by a Turing machine, then hypercomputation is trivially impossible in our universe.

The constants you're taking about are limits of computable numbers.  If all you have is a computer you can't produce such a number in finite time.

It sounds like you're taking two different things named after the same mathematician and assuming they're somehow connected when they're not.

(Disclaimer: I'm going off the information in the question alone.)