I do recall playing World of Tanks with a 800ms Ping. After about 3 months or so I was back to thinking there was no Ping until a problem with my ISP was fixed and I dropped to 8ms. After which I ran into walls a lot.
The brain can adapt to such things rather well, given enough time.
I remember when we upgraded from a 28.8k modem to ISDN. My Quake got a lot better purely because of lower latency. A friend was left behind on modem and he could tell the difference too, I was virtually unbeatable to him after the upgrade.
Of course we both knew that it was down to an unfair advantage so it wasn't a true victory.
I tried a few times and I can consistently make Windows miss at least the first keypress if I haven't opened the Start menu in a few minutes.
When the only source of latency is the extra ~16ms added by the composting, you likely can't feel it, but it adds up to other sources of latency that can make things feel bad more often. Such as:
-latency added by text editors depending on their quality and the amount of work they are doing (colors, intellisense, file size, etc).
-latency added by keyboards, some are worse than others
-latency added by monitors. Good ones are in the 1ms range but bad ones can be as high as 40
Sadly the latency on all of these fronts has generally been trending higher as computers have gotten more powerful.