An unloaded motor produces approximately 2.5%-3.0% more short circuit current than a fully loaded motor. I admit it is not much difference-nevertheless, it is a difference.
I offer the following references: Circuit Analysis of A.C. Power Systems by Edith Clarke Vol. II, page 220 and Analysis of Faulted Poer Systems by Paul Anderson,Iowa State University Press. page 226
First you construct the equivalent circuit of the induction motor being supplied by a source voltage of 1 per unit at an angle of zero degrees. By using the per unit motor impedances and angles, one can calculate the internal machine voltage and angle behind the motor reactance. On an unloaded motor, the internal voltage, which is called Em, is greater than the internal vlotage when this motor is fulled loaded. Also the power factor of an unloaded motor is considerably less than a motor which has load. An unloaded motor has a power factor of say .3, where a fully loaded motor has a power factor of .88 or higher. The internal machine voltage Em is responsible for the amount of short circuit current which can flow through the machine reactances to the fault. The higher the internal machine voltage, the greater the short circuti current.
When you construct a table of the calculations for various values of motor load, power factor and internal voltage, you can determine the short circuit current from the motor for various values of internal motor voltage.
In summary, an unloaded motor produces slightly more short circuit current than a fully loaded motor. However, the increase in curent is usually considered insignificant when compared to the other assumptions involved in making short circuit calculations.