It doesn't work, because the length you need to shorten to achieve a quarter-tone changes depending on which fret is is use (specifically, it would be 24th root of the length starting from the current fret). So if you were fretting in first position, the palm fret would give you roughly a semi-tone (slightly more), and if you were fretting in higher positions, it would be more than that. With some very careful planning, you could maybe use the spots that give you 3/4 or 5/4 tones.