Er, no. The studies I've read all end up showing that principled testing helps, but test-first and TDD (strict red/green cycle, code only enough to pass the new test, etc) provide no additional benefit over anything else that gets the tests written.

The "it depends" always comes from the echo chamber trying to justify their desire to believe that TDD isn't completely useless. It actually feels quite similar to the claims I've seen from practitioners that reikei, faith healing, etc aren't complete bunk.