Yes, and it is one of the better stress tests available precisely because it is unscripted. Quarterly reports get drafted, reviewed, and polished. A redemption request hits the desk without warning and the response is operational rather than curated.
The assumption doing the most work in your read is that the communication behavior you observed reflects the IR operation broadly, when it could reflect how that specific sponsor treats liquidity requests versus, say, a capital call or a material asset event. Those can produce entirely different communication patterns depending on whether the sponsor has written protocols or is improvising each time.
The risk you did not name is selection bias in the signal. A sponsor who handles a non-hostile liquidity request well may still fumble a contentious one, because the pressure dynamics are different. If the LP came in professionally and framed it as a need rather than a complaint, the sponsor's incentive to perform is high. The test is sharper when the request has some friction in it, a disputed timeline, an ambiguous clause in the PPM, a partial redemption ask on an illiquid structure. That is where process either exists or it does not.
For what it is worth, the specific things I would score in your scenario are: whether the initial acknowledgment gave a timeline or just confirmed receipt, whether interim updates arrived on the schedule they stated or required the LP to chase, and whether the sponsor's explanation of the mechanism matched what the operating agreement actually says. The last one is where I have seen the most divergence. A sponsor who paraphrases the redemption clause loosely under pressure either does not know it well or is managing the situation rather than the process.
The quarterly report comparison you draw is valid. Reports show what a sponsor chooses to disclose. Operational pressure shows what they actually have built.
What did the interim update cadence look like, and did it hold to whatever timeline they initially gave?