Yes, that works (to a good approximation) for low turns ratios and cartridges with low source impedances. However, with higher turns ratios and higher source impedances, it isn't accurate.
Take for example a cartridge with a source impedance of 40 ohms and a SUT with a turns ratio of 1:30. Say the cartridge has an output voltage of 0.2mV, and lets assume the transformer is perfect and therefore doesn't have any resistance in the coil windings, and it's fed into a phonostage with a 47k input impedance.
A step-up ratio of 1:30 and an output voltage of 0.2mV should give an output from the SUT of 6mV, right?
No, the output is actually only 3.4mV. The reason is because the cartridge sees a load of only 52 ohms and its own internal impedance is 40 ohms.