Not necessarily , for a given definition of AGI you could have mathematical proof that it is incomputable similar to how Gödel incompleteness theorems work .

It need not even be incomputable, it could be NP hard and practically be incomputable, or it could be undecidable I.e. a version of the halting problem.

There are any number of ways our current models of mathematics or computation can in theory could be shown as not capable of expressing AGI without needing a fundamental change in physics