With the warning that I am not an expert, see my answer below. While there is obviously thematic overlap between the Tractatus and Gödel, Wittgenstein himself viewed Gödel's work as fundamentally nonsensical. Now why the "nonsense" of the Tractatus is ok, while the "nonsense" of Gödel is not, is admittedly not clear, and we are under no obligation to respect it, but that would be (early) Wittgenstein's opinion.