No, it would not. It would require the LLM to provide a proof for the program that it outputs, which seems reasonable in the same way that a human decompiling a program would be able to provide a record of his/her reasoning.

The formal verifier would then merely check the provided proof, which is a simple mechanical process.

This is analogous to a mathematician providing a detailed proof and a computer checking it.

What is impossible due to undecidability is for two arbitrary programs, to either prove or disprove their equivalence. However, the two programs we are talking about are highly correlated, and thus not arbitrary at all with respect to each other. If an LLM is able to provide a correct decompilation, then in principle it should also be able to provide a proof of the correctness of that decompilation.