It very well be program dependent. What if found interesting though is the relationship between the brain and our sense of hearing and psychoacoustics. This is hard-wired. You cannot consciously override it or turn it off. This explains things like "expectation bias" and why you 100% absolutely will hear a difference in certain situations. The real proof in the pudding is to be able to pick these things out with accuracy in a controlled test situation.
I think perhaps the minimum takeaway for this is that few people are so have so mastered the craft of composition or songwriting that their time isn't better spent on polishing the piece of music itself, rather than obsessing on these sorts of details, and to prioritize.
I once had a disagreement with a house engineer at a local club. He didn't think my headset mic "technically" sounded as good as a decent stand mic. No argument there. But there were priorities. I can tell you that the certainly nobody in the club would know the difference. But because I play guitar while I sing, the headset allows me to be more interactive with the audience... go do different parts of the stage and sing. I'm not having to run back to a central spot on the stage all the time. Plus, on perhaps a subconscious level, a mic stand was barrier between myself and an audience. Singers who don't play an instrument can use a wireless handheld and they don't have this issue, but singing instrumentalists do. Bottom line was that the first night I used the wireless headset, my performance and ability to interact was so much better that audience thought it sounded better. I had people tell me it sounded better than ever. However, it was probably just that the performance was better and more engaging and that colored their perception. All in all, the benefits far outweighed the terrible, terrible reduction in quality going from an AKG headset to a Sennheiser handheld mic.

Just saying... one has to prioritize. There's a whole industry built on selling the idea that you just can't make music unless you have XYZ guitar or XYZ speakers. Many people are advanced and discriminating that it can make a difference, but it should never be used as a reason NOT to create.