I've played with VTA on the fly primarily with two carts. The first is a Denon DL-311LC MC that didn't always want to stay in the groove. I played with VTA see see if that would help, and fine tuned on the fly. Although I think this was primarily a compliance issue, fine tuning VTA allowed me to keep needle in the groove.
With this experiment I realized the ease of adjusting VTA on the fly, and so also tried it with my Nag MM cart. I started at prescribed height, then fine tuned while playing. I intentionally went up and down from baseline in order to see if I could hear the difference. While I wouldn't say the sound differences were huge, I could detect small changes that I might have never noticed if I hadn't played with this at all. The further I got from prescribed height in either direction, the less "right" it sounded, like the cart was "thinner" sounding. I ended up just a fraction (like .25 mm) higher than prescribed setting. So while my methods weren't scientific, and may have been prejudiced by the record I had on at the time, etc..., the fact I was able to conduct this experiment at all is an uncommon experience among tonearms.