Would Schmidhuber's theories of everything be capable of performing hypercomputation? Jürgen Schmidhuber pointed out that a simple explanation of the universe would be a Turing machine analogy programmed to execute all possible programs computing all possible histories for all types of computable physical laws. His work was based on Zuse's thesis.

This hypothesis would be inside the domain of Digital Physics, a group of hypothetical models that propose that the universe is analogous to a computer or an automata. 

(https://en.wikipedia.org/wiki/Digital_physics)

In 2000, he expanded this work by combining Ray Solomonoff's theory of inductive inference with the assumption that quickly computable universes are more likely than others. This work on digital physics also led to limit-computable generalizations of algorithmic information or Kolmogorov complexity and the concept of Super Omegas, which are limit-computable numbers that are even more random (in a certain sense) than Gregory Chaitin's number of wisdom Omega.

So since Chaitin's constant (https://en.wikipedia.org/wiki/Chaitin%27s_constant) would allow hypercomputation if it existed in the pysics of the universe, would then Schmidhuber's hypothesis be able to perform hypercomputation?
Also, in the hytpercomputation wikipedia entry (https://en.wikipedia.org/wiki/Hypercomputation) it says (In "eventually correct" systems):


  A symbol sequence is computable in the limit if there is a finite, possibly non-halting program on a universal Turing machine that incrementally outputs every symbol of the sequence. This includes the dyadic expansion of π and of every other computable real, but still excludes all noncomputable reals. Traditional Turing machines cannot edit their previous outputs; generalized Turing machines, as defined by Jürgen Schmidhuber, can. He defines the constructively describable symbol sequences as those that have a finite, non-halting program running on a generalized Turing machine, such that any output symbol eventually converges; that is, it does not change any more after some finite initial time interval. Due to limitations first exhibited by Kurt Gödel (1931), it may be impossible to predict the convergence time itself by a halting program, otherwise the halting problem could be solved. Schmidhuber uses this approach to define the set of formally describable or constructively computable universes or constructive theories of everything. Generalized Turing machines can eventually converge to a correct solution of the halting problem by evaluating a Specker sequence.


And also, Super-recursive algorithms are closely related to hypercomputation, and super recursive algorithm is just one way of defining hypercomputation. In super-recursive algorithms wikipedia entry (https://en.wikipedia.org/wiki/Super-recursive_algorithm), Schmidhuber's model is included as a super-recursive algorithm-based model

So, knowing all of this, then, would Schmidhuber's hypothetical universes be based on 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.)