I know that the power factor of an induction motor varies with load and is very low at no load and high at full load, but does the reactive power vary as well? If so, how much can it vary?
When the load decreases, the power factor decreases primarily due to the decrease in real power. Reactive power is primarily due to the magnetizing current, But there is a small amount due to the stator and rotor leakage reactances. Magnetizing current depends on the voltage across the magnetizing branch of the equivalent circuit that will increase slightly with reduced load because the voltage drop across the stator resistance and leakage reactance declines when the current declines due to reduced load.
In the equivalent circuit shown below, R1 & X1 are the stator resistance and leakage reactance, Gc and Bm are the magnetizing branch, and X2 is the rotor leakage reactance. R2/s represents the rotor resistance combined with a variable resistance that represents the mechanical load.
The following motor performance data shows quite a significantly decreasing reactive VA as the motor load declines to zero. The slight increase in magnetizing VA must be insignificant compared to the loss of reactive VA in the rotor branch as the rotor current drops to near zero.