Is it possible to also measure the audio susceptibility (Vout/Vin) of a power supply with the current injector J2111A? 

Yes.  The J2111A is a small signal current injector.  We do often use it to non-invasively perform a PSRR measurement.  Since every power source presents finite impedance, the small signal current perturbation of the regulator input source from the J2111A will result in a voltage signal at the regulator input.  The output and input signals can then be easily measured for PSRR.  However, we also offer an injector for this purpose, the J2120A.