What if a galaxy was not tilted but was positioned toward us perfectly face-on, so stars in the galaxy are neither approaching nor receding from us, from our point of view. would the tully-fisher technique work?

In astronomy, the Tully– Fisher relation (TFR) is an exact connection between the mass or characteristic radiance of a winding world and its precise speed or discharge line width. So the appropriate response is NO, there is no movement towards or far from us. For this situation, there is no Doppler effect we can quantify.