No, incompleteness and its generalizations fall within computability theory, not complexity theory.
In regard to your second point, you say "other problems in computational complexity". Again, you mentioned computability theory, not CCT. They are different endeavors. Aaronson was careful to say that this is not another essay on philosophy and computability.
In regard to your second point, you say "other problems in computational complexity". Again, you mentioned computability theory, not CCT. They are different endeavors. Aaronson was careful to say that this is not another essay on philosophy and computability.