Thing about it: what we tend to hear the most, for determining/identifying instrument timbres for instance, is the sound of a note's attack. See the work done by J-C Risset, Mathews, and I'm sure by now many others for example.
We test equipment with long duration sinusoids mostly. Then sometimes now we test with tone bursts, quasi-impulses, pseudorandom noise, and various sorts of swept signals (see for example the Farina stuff in the tubular thread nearby).
The way that a compressor's attack/release function works is difficult to quantify and key to how well it preserves, or how it modifies, the source material. The steady-state degree of compression is an important parameter, but won't tell you about the way you got there.
Not to say it can't be done, but it's non-trivial.