I feel like that would fail. The reason is that Gödel numbers are rather arbitrary, and will therefore be rather far from a form that insights can be gleaned from. They are a representation of a representation, using the fundamental theorem of arithmetic only as a trick to encode any string of symbols into one integer.

As an example of just how arbitrary Gödel numbers are, consider the expressions `((3*n)+1)` and `((n*3)+1)`. Those expressions are clearly equivalent, yet the Gödel numbers for those two expressions are wildly different, with a relation that is rather complex.

IIUC Gödel himself never "used" or analyzed Gödel numbers as such, only the idea that they could be constructed.