Diffraction would have an adverse impact beyond f/8, but it may be offset by DOF benefits. Diffraction can also reduce the likelihood of moire.
If a bare lens needs AF Fine Tuning of -15, it's possible that with a teleconverter the adjustment is -5, so that lens could be closer to ideal with a teleconverter. Using a higher aperture would mask the AF error with improved DOF even after considering the impact of diffraction. So it is certainly possible that on some lens/camera/teleconverter combinations you would have better performance with a teleconverter and at f/16 than with a bare lens at f/2.8. This is not typical - but certainly possible. You might get different results with different target distances or different lighting. And the testing shows that it is important to know how your gear performs.