The last time I looked briefly at the "hot hands" idea, there had been multiple studies after the initial one from 1985. Some of the studies had found an effect and others had not.
I think it is very hard to do a statistically meaningful study in real-life competitive situations. The conditions are often poorly controlled. For me the real question is: Numerically, how large is the effect? Does a basketball player switch from 40% to 70% when he moves to the zone?
And as the article linked above points out, the statistics needs to be done right. According to the article, the original study had a major error in how the data was analyzed.
The largest dataset I know of for pool is John Schmidt's high run attempts that took place over months. Unfortunately, only runs of 100 or more were recorded. The distribution of runs was more or less as expected for independent events (no hot hands). His 626 was somewhat unexpected in that based on his average accuracy, there was only a 25% chance that he would have had a 626 in as many attempts as he took.
Jayson Shaw's run of 714 starts to be interesting, but there's not enough data to make a good case.