There is a direct mathematical correlation, in fact. And the more voltage gain afforded by a SUT, the lower the impedance seen by the cartridge, which will be the input impedance of the phono stage (usually 47K ohms) divided by the square of the turns ratio (which is synonymous with voltage gain).
@lewm is absolutely correct. My SUT allows both 15:1 and 10:1 turns ratios, and therefore allows a 47kΩ MM input to be seen as either 208Ω or 470Ω. It makes a difference!