The QC (or any similar device) can only capture what are technically LTI (linear and time invariant) devices. In other words, things like gain stages, amplifiers, and speakers that theoretically respond the same way to a signal no matter the level of that signal, no matter what time. In the case of things like compression, the gain response changes depending on the level of the incoming signal, and the time transfer function of how it reduces that gain is often different depending on the incoming signal level, peaky-ness (crest factor, or how narrow the waveform transient is), and frequency response. This is complex and changes dramatically with time and input signal complexity, so there is no way to capture a compressor accurately. You can capture it in terms of the process, but what you get out the other side will be nothing like how your compressor sounds.