Not necessarily. If you add new code to the user signup (let's say some additional checks on the shape of their username) and the integration test for the happy path of a user signup still passes, the new code is absolutely covered by existing tests (though probably not completely, there are probably edge cases not covered).

The tests/types correspondence still holds: if you write new code, you will often also need to alter the types to correctly describe the changed domain. In the username example above, after adding username validation it would be a good idea to have a dedicated `Username` type that can only contain valid usernames instead of just stuffing everything into `String`. If you count extra time writing and refactoring tests after adding new code, you should also count the extra time writing and refactoring additional types after adding new code.